{"id":65382,"date":"2026-08-10T14:47:00","date_gmt":"2026-08-10T13:47:00","guid":{"rendered":"https:\/\/blog-admin.thethinkacademy.com\/?p=65382"},"modified":"2026-08-10T14:47:01","modified_gmt":"2026-08-10T13:47:01","slug":"acute-triangle-and-obtuse-triangle-guide","status":"publish","type":"post","link":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/","title":{"rendered":"Acute and Obtuse Triangles Explained: Definitions, Properties and Examples"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Every triangle belongs to one of three categories based on its angles: acute, right, or obtuse. Knowing which category a triangle belongs to \u2014 and why \u2014 is foundational geometry knowledge that appears in school assessments from Grade 5 through Grade 9, in EQAO, and in every major Canadian mathematics competition including the Gauss Contest and AMC 8. This guide covers the definitions clearly, explains how to identify each type from angles and side lengths, and works through the types of problems where these concepts are tested.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">The Three Types of Triangles by Angle<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Triangles are classified by their largest angle:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Type<\/th><th>Condition<\/th><th>Largest angle<\/th><\/tr><\/thead><tbody><tr><td><strong>Acute triangle<\/strong><\/td><td>All three angles are less than 90\u00b0<\/td><td>&lt; 90\u00b0<\/td><\/tr><tr><td><strong>Right triangle<\/strong><\/td><td>One angle equals exactly 90\u00b0<\/td><td>= 90\u00b0<\/td><\/tr><tr><td><strong>Obtuse triangle<\/strong><\/td><td>One angle is greater than 90\u00b0<\/td><td>&gt; 90\u00b0<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Every triangle fits exactly one of these categories. A triangle cannot be both acute and obtuse, and a triangle can have at most one right angle or one obtuse angle (since all three angles must sum to 180\u00b0).<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Acute Triangle and Obtuse Triangle Guide: What Is an Acute Triangle?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">An <strong>acute triangle<\/strong> is a triangle in which <strong>all three angles are less than 90\u00b0<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Every angle in an acute triangle is acute \u2014 no right angles, no obtuse angles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Examples of acute triangles:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Equilateral triangle (all angles = 60\u00b0) \u2014 always acute<\/li>\n\n\n\n<li>A triangle with angles 50\u00b0, 60\u00b0, and 70\u00b0 \u2014 all less than 90\u00b0, so acute<\/li>\n\n\n\n<li>A triangle with angles 45\u00b0, 75\u00b0, and 60\u00b0 \u2014 all less than 90\u00b0, so acute<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Key properties of acute triangles:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>All three altitudes (perpendicular lines from each vertex to the opposite side) fall <strong>inside<\/strong> the triangle<\/li>\n\n\n\n<li>The circumcentre (centre of the circumscribed circle) falls <strong>inside<\/strong> the triangle<\/li>\n\n\n\n<li>The orthocentre (intersection of the altitudes) falls <strong>inside<\/strong> the triangle<\/li>\n\n\n\n<li>For sides a \u2264 b \u2264 c: a\u00b2 + b\u00b2 > c\u00b2 (the Pythagorean theorem inequality for acute triangles)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>How to recognise an acute triangle from its angles:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you know all three angles: check that each is less than 90\u00b0.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you know only the side lengths: use the inequality a\u00b2 + b\u00b2 &gt; c\u00b2 where c is the longest side.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Acute Triangle and Obtuse Triangle Guide: What Is an Obtuse Triangle?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">An <strong>obtuse triangle<\/strong> is a triangle in which <strong>one angle is greater than 90\u00b0<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Only one angle can be obtuse \u2014 if one angle is greater than 90\u00b0, the other two must sum to less than 90\u00b0, making them both acute.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Examples of obtuse triangles:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A triangle with angles 120\u00b0, 35\u00b0, and 25\u00b0 \u2014 120\u00b0 > 90\u00b0, so obtuse<\/li>\n\n\n\n<li>A triangle with angles 100\u00b0, 50\u00b0, and 30\u00b0 \u2014 100\u00b0 > 90\u00b0, so obtuse<\/li>\n\n\n\n<li>A triangle with angles 91\u00b0, 60\u00b0, and 29\u00b0 \u2014 91\u00b0 > 90\u00b0, so obtuse (barely)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Key properties of obtuse triangles:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The altitude from the vertex with the obtuse angle falls <strong>inside<\/strong> the triangle, but the altitudes from the other two vertices fall <strong>outside<\/strong> (requiring the sides to be extended)<\/li>\n\n\n\n<li>The circumcentre falls <strong>outside<\/strong> the triangle<\/li>\n\n\n\n<li>The orthocentre falls <strong>outside<\/strong> the triangle<\/li>\n\n\n\n<li>For sides a \u2264 b \u2264 c: a\u00b2 + b\u00b2 &lt; c\u00b2 (the Pythagorean theorem inequality for obtuse triangles)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>How to recognise an obtuse triangle from its angles:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you know all three angles: check that one exceeds 90\u00b0.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">If you know only the side lengths: check a\u00b2 + b\u00b2 vs c\u00b2 where c is the longest side.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If a\u00b2 + b\u00b2 > c\u00b2: acute<\/li>\n\n\n\n<li>If a\u00b2 + b\u00b2 = c\u00b2: right<\/li>\n\n\n\n<li>If a\u00b2 + b\u00b2 &lt; c\u00b2: obtuse<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">The Angle-Side Relationship: Identifying Triangle Type from Side Lengths<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">This is the most practically useful skill for geometry problems: identifying whether a triangle is acute, right, or obtuse without being given the angles directly.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The rule:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For a triangle with sides a, b, c where c is the longest side:<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>a<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><msup><mi>b<\/mi><mn>2<\/mn><\/msup><mo>\u2277<\/mo><msup><mi>c<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">a^2 + b^2 \\gtrless c^2<\/annotation><\/semantics><\/math>a2+b2\u2277c2<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If a\u00b2 + b\u00b2 <strong>><\/strong> c\u00b2: <strong>acute triangle<\/strong><\/li>\n\n\n\n<li>If a\u00b2 + b\u00b2 <strong>=<\/strong> c\u00b2: <strong>right triangle<\/strong><\/li>\n\n\n\n<li>If a\u00b2 + b\u00b2 <strong>&lt;<\/strong> c\u00b2: <strong>obtuse triangle<\/strong><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Why this works:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This follows from the law of cosines: c\u00b2 = a\u00b2 + b\u00b2 \u2212 2ab cos(C), where C is the angle opposite the longest side c.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If C &lt; 90\u00b0: cos(C) > 0, so c\u00b2 &lt; a\u00b2 + b\u00b2 \u2192 acute<\/li>\n\n\n\n<li>If C = 90\u00b0: cos(C) = 0, so c\u00b2 = a\u00b2 + b\u00b2 \u2192 right<\/li>\n\n\n\n<li>If C > 90\u00b0: cos(C) &lt; 0, so c\u00b2 > a\u00b2 + b\u00b2 \u2192 obtuse<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.thinkacademy.ca\/free-assessment?source_id=6721&amp;source_type=9&amp;utm_medium=website&amp;utm_source=pc_blog\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"409\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_39_01-PM-1-1024x409.png\" alt=\"\" class=\"wp-image-65384\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_39_01-PM-1-1024x409.png 1024w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_39_01-PM-1-300x120.png 300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_39_01-PM-1-768x307.png 768w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_39_01-PM-1-1536x614.png 1536w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_39_01-PM-1-1300x520.png 1300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_39_01-PM-1.png 1983w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Recognising triangle types is only the beginning. Our free online assessment shows how confidently your child applies math concepts to unfamiliar problems\u2014and identifies the areas that need more work.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em><a href=\"https:\/\/www.thinkacademy.ca\/free-assessment?source_id=6721&amp;source_type=9&amp;utm_medium=website&amp;utm_source=pc_blog\">Get your child\u2019s free feedback report \u2192<\/a><\/em><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Acute Triangle and Obtuse Triangle Guide: Worked Examples<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Example 1 \u2014 Identifying from angles<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Classify each triangle:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a) Angles: 40\u00b0, 75\u00b0, 65\u00b0 All less than 90\u00b0. <strong>Acute triangle.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b) Angles: 90\u00b0, 45\u00b0, 45\u00b0 One angle equals 90\u00b0. <strong>Right triangle.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c) Angles: 110\u00b0, 40\u00b0, 30\u00b0 One angle exceeds 90\u00b0. <strong>Obtuse triangle.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d) Angles: 60\u00b0, 60\u00b0, 60\u00b0 All equal 60\u00b0. <strong>Acute triangle (equilateral).<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Example 2 \u2014 Identifying from side lengths<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Classify each triangle with the given side lengths:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a) Sides: 5, 7, 9 Longest side: c = 9. Check: 5\u00b2 + 7\u00b2 = 25 + 49 = 74 vs 9\u00b2 = 81. 74 &lt; 81, so a\u00b2 + b\u00b2 &lt; c\u00b2. <strong>Obtuse triangle.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b) Sides: 5, 12, 13 Longest side: c = 13. Check: 5\u00b2 + 12\u00b2 = 25 + 144 = 169 = 13\u00b2. Equal. <strong>Right triangle.<\/strong> (This is the (5, 12, 13) Pythagorean triple.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c) Sides: 6, 7, 8 Longest side: c = 8. Check: 6\u00b2 + 7\u00b2 = 36 + 49 = 85 vs 8\u00b2 = 64. 85 &gt; 64, so a\u00b2 + b\u00b2 &gt; c\u00b2. <strong>Acute triangle.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">d) Sides: 3, 4, 6 Longest side: c = 6. Check: 3\u00b2 + 4\u00b2 = 9 + 16 = 25 vs 6\u00b2 = 36. 25 &lt; 36. <strong>Obtuse triangle.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Example 3 \u2014 Finding a missing angle<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>A triangle has angles x, 2x, and 3x. Classify it.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sum of angles = 180\u00b0: x + 2x + 3x = 180\u00b0 \u2192 6x = 180\u00b0 \u2192 x = 30\u00b0.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angles: 30\u00b0, 60\u00b0, 90\u00b0. One angle equals 90\u00b0. <strong>Right triangle.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Example 4 \u2014 Word problem<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The three sides of a triangle are 8 cm, 15 cm, and 17 cm. Is the triangle acute, right, or obtuse? What is its area?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Longest side: 17. Check: 8\u00b2 + 15\u00b2 = 64 + 225 = 289 = 17\u00b2.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This is the (8, 15, 17) Pythagorean triple \u2014 a <strong>right triangle<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Area = (1\/2) \u00d7 base \u00d7 height = (1\/2) \u00d7 8 \u00d7 15 = <strong>60 cm\u00b2.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(In a right triangle, the two legs are the base and height.)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Special Cases and Common Misconceptions<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Can an equilateral triangle be obtuse?<\/strong> No. An equilateral triangle has all angles equal to 60\u00b0, which are all acute. Every equilateral triangle is acute.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Can an isosceles triangle be obtuse?<\/strong> Yes. An isosceles triangle has two equal angles. If those two equal angles are each 30\u00b0 (summing to 60\u00b0), the third angle is 120\u00b0 \u2014 obtuse. Example: a triangle with angles 30\u00b0, 30\u00b0, 120\u00b0 is both isosceles and obtuse.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Can a triangle have two obtuse angles?<\/strong> No. Two angles greater than 90\u00b0 would sum to more than 180\u00b0, making a third positive angle impossible. Every triangle has at most one obtuse angle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Is a right triangle acute or obtuse?<\/strong> Neither. Right triangles form their own category. The definitions of acute and obtuse triangles specifically exclude the case where an angle equals exactly 90\u00b0.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>A very &#8220;flat&#8221; triangle \u2014 is it obtuse?<\/strong> Usually yes. A triangle with angles 170\u00b0, 5\u00b0, 5\u00b0 is obtuse. Very flat triangles typically have one very large obtuse angle.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Acute Triangle and Obtuse Triangle Guide: EQAO and Canadian Mathematics Competitions<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>EQAO Grade 3 and Grade 6:<\/strong> Triangle classification \u2014 acute, right, obtuse \u2014 is explicitly tested in EQAO&#8217;s spatial sense strand. Students are expected to identify triangle types by looking at angles and to understand that the properties of each type are distinct. See our <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/05\/26\/eqao-grade-6-complete-guide-ontario\/\">EQAO Grade 6 complete guide<\/a> and <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/05\/27\/eqao-grade-3-complete-guide-ontario\/\">EQAO Grade 3 complete guide<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Gauss Contest (CEMC, Grades 7\u20138):<\/strong> Triangle geometry \u2014 including classification and area calculations \u2014 appears in Part A and Part B of the Gauss Contest. A common problem type: given side lengths or angle relationships, determine the triangle type and use its properties to find an unknown measurement. Students who know the a\u00b2 + b\u00b2 comparison rule can solve these much faster than those who work from angle sums alone. See our <a href=\"https:\/\/www.thinkacademy.ca\/blog\/blog\/2026\/05\/05\/gauss-math-contest-complete-guide-canada\/\">Gauss math contest guide<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>AMC 8:<\/strong> Triangle type problems appear regularly in the AMC 8 geometry section. They often combine classification with area calculations, the Pythagorean theorem, or coordinate geometry. Recognising a Pythagorean triple in the side lengths \u2014 and therefore knowing the triangle is right \u2014 is one of the most common time-saving shortcuts in AMC 8 geometry. See our <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/04\/15\/amc-8-math-competition-guide-for-parents\/\">AMC 8 guide<\/a>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Cayley and Pascal Contests (Grades 9\u201310):<\/strong> At this level, acute and obtuse triangle classification appears as a component in larger geometry problems \u2014 often combined with the law of cosines, area calculations using different formulas, or coordinate geometry applications. The a\u00b2 + b\u00b2 comparison rule is assumed knowledge.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For more on the Pythagorean triples that make many of these problems faster to solve, see our <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/pythagorean-triples-guide\/\">Pythagorean triples guide<\/a>. For the triangle inequality theorem \u2014 the result governing which side lengths can form any triangle at all \u2014 see our <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/triangle-inequality-theorem-guide\/\">triangle inequality theorem guide<\/a>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.thinkacademy.ca\/free-assessment?source_id=6721&amp;source_type=9&amp;utm_medium=website&amp;utm_source=pc_blog\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"409\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_41_45-PM-1-1024x409.png\" alt=\"Acute Triangle and Obtuse Triangle Guide cta\" class=\"wp-image-65385\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_41_45-PM-1-1024x409.png 1024w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_41_45-PM-1-300x120.png 300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_41_45-PM-1-768x307.png 768w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_41_45-PM-1-1536x614.png 1536w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_41_45-PM-1-1300x520.png 1300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_41_45-PM-1.png 1983w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Triangle classification appears in EQAO, Gauss and AMC 8\u2014but stronger questions combine it with side lengths, area and logical reasoning. Your child can take a free online assessment and receive a personalised report showing their strengths and learning gaps.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.thinkacademy.ca\/free-assessment?source_id=6721&amp;source_type=9&amp;utm_medium=website&amp;utm_source=pc_blog\">Start the free assessment \u2192<\/a><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Practice Problems<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Set A \u2014 Identifying triangle type from angles<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Angles: 55\u00b0, 65\u00b0, 60\u00b0 \u2192 ___<\/li>\n\n\n\n<li>Angles: 90\u00b0, 30\u00b0, 60\u00b0 \u2192 ___<\/li>\n\n\n\n<li>Angles: 120\u00b0, 35\u00b0, 25\u00b0 \u2192 ___<\/li>\n\n\n\n<li>Angles: 45\u00b0, 45\u00b0, 90\u00b0 \u2192 ___<\/li>\n\n\n\n<li>Angles: 80\u00b0, 80\u00b0, 20\u00b0 \u2192 ___<\/li>\n\n\n\n<li>Angles: 89\u00b0, 89\u00b0, 2\u00b0 \u2192 ___<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Set B \u2014 Identifying triangle type from side lengths<\/strong><\/p>\n\n\n\n<ol start=\"7\" class=\"wp-block-list\">\n<li>Sides: 3, 4, 5 \u2192 ___<\/li>\n\n\n\n<li>Sides: 6, 8, 11 \u2192 ___<\/li>\n\n\n\n<li>Sides: 5, 6, 7 \u2192 ___<\/li>\n\n\n\n<li>Sides: 8, 15, 17 \u2192 ___<\/li>\n\n\n\n<li>Sides: 7, 7, 7 \u2192 ___<\/li>\n\n\n\n<li>Sides: 4, 4, 6 \u2192 ___<\/li>\n\n\n\n<li>Sides: 2, 3, 4 \u2192 ___<\/li>\n\n\n\n<li>Sides: 9, 12, 15 \u2192 ___<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Set C \u2014 Mixed problems<\/strong><\/p>\n\n\n\n<ol start=\"15\" class=\"wp-block-list\">\n<li>A triangle has angles x, x + 10\u00b0, and x + 20\u00b0. What type is it?<\/li>\n\n\n\n<li>A triangle has two angles of 70\u00b0 each. Is it acute, right, or obtuse? What is the third angle?<\/li>\n\n\n\n<li>A right triangle has one leg of 9 and a hypotenuse of 15. What is the other leg? Is the original triangle with sides 9, 15, and this leg acute, right, or obtuse?<\/li>\n\n\n\n<li>Can a triangle with sides 5, 5, and 10 exist? If not, why not?<\/li>\n\n\n\n<li>A triangle has angles in the ratio 1:2:3. What type is it?<\/li>\n\n\n\n<li>The longest side of a triangle is 10. The other two sides are equal. What is the range of the equal side lengths for which the triangle is acute?<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Answers:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Set A:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Acute \u00a0 2) Right \u00a0 3) Obtuse \u00a0 4) Right \u00a0 5) Acute \u00a0 6) Acute (all angles &lt; 90\u00b0, even though two are close to 90\u00b0)<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">Set B: 7) 3\u00b2 + 4\u00b2 = 25 = 5\u00b2 \u2192 <strong>Right<\/strong> 8) 6\u00b2 + 8\u00b2 = 100 vs 11\u00b2 = 121. 100 &lt; 121 \u2192 <strong>Obtuse<\/strong> 9) 5\u00b2 + 6\u00b2 = 61 vs 7\u00b2 = 49. 61 &gt; 49 \u2192 <strong>Acute<\/strong> 10) 8\u00b2 + 15\u00b2 = 289 = 17\u00b2 \u2192 <strong>Right<\/strong> (Pythagorean triple) 11) 7\u00b2 + 7\u00b2 = 98 vs 7\u00b2 = 49. 98 &gt; 49 \u2192 <strong>Acute<\/strong> (equilateral) 12) 4\u00b2 + 4\u00b2 = 32 vs 6\u00b2 = 36. 32 &lt; 36 \u2192 <strong>Obtuse<\/strong> 13) 2\u00b2 + 3\u00b2 = 13 vs 4\u00b2 = 16. 13 &lt; 16 \u2192 <strong>Obtuse<\/strong> 14) 9\u00b2 + 12\u00b2 = 225 = 15\u00b2. <strong>Right<\/strong> (3 \u00d7 (3,4,5) Pythagorean triple)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Set C: 15) x + (x+10) + (x+20) = 180 \u2192 3x + 30 = 180 \u2192 x = 50. Angles: 50\u00b0, 60\u00b0, 70\u00b0. All &lt; 90\u00b0 \u2192 <strong>Acute<\/strong> 16) 70\u00b0 + 70\u00b0 + third = 180\u00b0 \u2192 third = 40\u00b0. All angles &lt; 90\u00b0 \u2192 <strong>Acute<\/strong> 17) 9\u00b2 + b\u00b2 = 15\u00b2 \u2192 b\u00b2 = 225 \u2212 81 = 144 \u2192 b = 12. Triangle (9, 12, 15) = 3 \u00d7 (3,4,5) \u2192 <strong>Right<\/strong> 18) Triangle inequality: 5 + 5 = 10, not strictly greater than 10. <strong>Does not exist<\/strong> \u2014 degenerate (collinear points) 19) Angles in ratio 1:2:3 sum to 180\u00b0. Parts: 30\u00b0, 60\u00b0, 90\u00b0. One angle = 90\u00b0 \u2192 <strong>Right<\/strong> 20) For acute with longest side 10 and equal sides s: need s\u00b2 + s\u00b2 &gt; 10\u00b2 \u2192 2s\u00b2 &gt; 100 \u2192 s &gt; 5\u221a2 \u2248 7.07. Also triangle inequality: s + s &gt; 10 \u2192 s &gt; 5. And each s &lt; 10 (otherwise s &gt; 10 becomes longest side). Combined: <strong>5\u221a2 &lt; s &lt; 10<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Frequently Asked Questions<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>What is an acute triangle?<\/strong> A triangle in which all three interior angles are less than 90\u00b0. Every angle is acute \u2014 there are no right or obtuse angles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>What is an obtuse triangle?<\/strong> A triangle in which one interior angle is greater than 90\u00b0. Only one angle can be obtuse (since the three angles must sum to 180\u00b0).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>How do you tell if a triangle is acute or obtuse from its sides?<\/strong> Let c be the longest side. Compare a\u00b2 + b\u00b2 with c\u00b2: if a\u00b2 + b\u00b2 &gt; c\u00b2, the triangle is acute; if equal, right; if a\u00b2 + b\u00b2 &lt; c\u00b2, obtuse.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Can a triangle be both acute and isosceles?<\/strong> Yes. An equilateral triangle (all sides equal, all angles 60\u00b0) is both equilateral and acute. Any isosceles triangle with angles 70\u00b0, 70\u00b0, 40\u00b0 is both isosceles and acute.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Can a triangle be both obtuse and isosceles?<\/strong> Yes. A triangle with angles 100\u00b0, 40\u00b0, 40\u00b0 is both obtuse and isosceles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>What is the difference between an acute angle and an acute triangle?<\/strong> An acute angle is a single angle less than 90\u00b0. An acute triangle is a triangle in which all three of its angles are acute (all less than 90\u00b0).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Do acute and obtuse triangles appear in mathematics competitions?<\/strong> Yes \u2014 in the Gauss Contest and AMC 8 regularly, and in more advanced form in the Cayley, Pascal, and Euclid Contests. The a\u00b2 + b\u00b2 comparison rule for identifying triangle type from side lengths is one of the most practical shortcuts in competition geometry.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><em>See our related guides: <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/triangle-inequality-theorem-guide\/\">triangle inequality theorem guide<\/a> \u00b7 <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/pythagorean-triples-guide\/\">Pythagorean triples guide<\/a> \u00b7 <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/05\/20\/special-triangles-in-trigonometry-guide\/\">special triangles in trigonometry<\/a> \u00b7 <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/04\/15\/amc-8-math-competition-guide-for-parents\/\">AMC 8 guide<\/a> \u00b7 <a href=\"https:\/\/www.thinkacademy.ca\/blog\/blog\/2026\/05\/05\/gauss-math-contest-complete-guide-canada\/\">Gauss math contest guide<\/a> \u00b7 <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/05\/26\/eqao-grade-6-complete-guide-ontario\/\">EQAO Grade 6 complete guide<\/a> \u00b7 <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/05\/27\/eqao-grade-3-complete-guide-ontario\/\">EQAO Grade 3 complete guide<\/a> \u00b7 <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/06\/06\/grade-7-math-curriculum-ontario\/\">Grade 7 math curriculum Ontario<\/a> \u00b7 <a href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/06\/22\/math-enrichment\/\">math enrichment guide<\/a><\/em><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Geometry fundamentals unlock everything that comes after. Build them properly.<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><a href=\"https:\/\/www.thinkacademy.ca\/trialclass_en?source_id=6721&amp;source_type=9&amp;utm_medium=website&amp;utm_source=pc_blog\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"409\" src=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_42_59-PM-1-1024x409.png\" alt=\"\" class=\"wp-image-65386\" srcset=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_42_59-PM-1-1024x409.png 1024w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_42_59-PM-1-300x120.png 300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_42_59-PM-1-768x307.png 768w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_42_59-PM-1-1536x614.png 1536w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_42_59-PM-1-1300x520.png 1300w, https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_42_59-PM-1.png 1983w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/a><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">If your child understands the definitions but gets stuck when problems combine several concepts, a guided lesson can help. Book a free online trial and see how Think Academy develops deeper mathematical reasoning.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><a href=\"https:\/\/www.thinkacademy.ca\/trialclass_en?source_id=6721&amp;source_type=9&amp;utm_medium=website&amp;utm_source=pc_blog\"><em>Book a free online trial lesson \u2192<\/em><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Every triangle belongs to one of three categories based on its angles: acute, right, or obtuse. &hellip; <a title=\"Acute and Obtuse Triangles Explained: Definitions, Properties and Examples\" class=\"hm-read-more\" href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/\"><span class=\"screen-reader-text\">Acute and Obtuse Triangles Explained: Definitions, Properties and Examples<\/span>Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":65383,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1752,17160,17135],"tags":[],"class_list":["post-65382","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-competitions","category-math-skills","category-study-tips-and-tools"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v25.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Acute Triangle and Obtuse Triangle: Definitions and Examples<\/title>\n<meta name=\"description\" content=\"An acute triangle and obtuse triangle guide \u2014 how to identify them, and practice problems including contest geometry.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Acute Triangle and Obtuse Triangle: Definitions and Examples\" \/>\n<meta property=\"og:description\" content=\"An acute triangle and obtuse triangle guide \u2014 how to identify them, and practice problems including contest geometry.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/\" \/>\n<meta property=\"og:site_name\" content=\"Think Academy Canada Blog\" \/>\n<meta property=\"article:published_time\" content=\"2026-08-10T13:47:00+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2026-08-10T13:47:01+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_28_56-PM-1.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1448\" \/>\n\t<meta property=\"og:image:height\" content=\"1086\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Think Academy\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Think Academy\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"12 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/\",\"url\":\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/\",\"name\":\"Acute Triangle and Obtuse Triangle: Definitions and Examples\",\"isPartOf\":{\"@id\":\"https:\/\/blog-admin.thethinkacademy.com\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/#primaryimage\"},\"image\":{\"@id\":\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_28_56-PM-1.png\",\"datePublished\":\"2026-08-10T13:47:00+00:00\",\"dateModified\":\"2026-08-10T13:47:01+00:00\",\"author\":{\"@id\":\"https:\/\/blog-admin.thethinkacademy.com\/#\/schema\/person\/5e5752520edd7febcc1056443eab8850\"},\"description\":\"An acute triangle and obtuse triangle guide \u2014 how to identify them, and practice problems including contest geometry.\",\"breadcrumb\":{\"@id\":\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/#primaryimage\",\"url\":\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_28_56-PM-1.png\",\"contentUrl\":\"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_28_56-PM-1.png\",\"width\":1448,\"height\":1086},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/blog-admin.thethinkacademy.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Acute and Obtuse Triangles Explained: Definitions, Properties and Examples\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/blog-admin.thethinkacademy.com\/#website\",\"url\":\"https:\/\/blog-admin.thethinkacademy.com\/\",\"name\":\"Think Academy Canada Blog\",\"description\":\"\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/blog-admin.thethinkacademy.com\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/blog-admin.thethinkacademy.com\/#\/schema\/person\/5e5752520edd7febcc1056443eab8850\",\"name\":\"Think Academy\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/blog-admin.thethinkacademy.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f79e3f7bff09863820040f04b26b5731542ae3733cf505c30733842df6e7ff82?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f79e3f7bff09863820040f04b26b5731542ae3733cf505c30733842df6e7ff82?s=96&d=mm&r=g\",\"caption\":\"Think Academy\"},\"sameAs\":[\"https:\/\/blog-admin.thethinkacademy.com\"],\"url\":\"https:\/\/blog-admin.thethinkacademy.com\/blog\/author\/thinkacademy\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Acute Triangle and Obtuse Triangle: Definitions and Examples","description":"An acute triangle and obtuse triangle guide \u2014 how to identify them, and practice problems including contest geometry.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/","og_locale":"en_US","og_type":"article","og_title":"Acute Triangle and Obtuse Triangle: Definitions and Examples","og_description":"An acute triangle and obtuse triangle guide \u2014 how to identify them, and practice problems including contest geometry.","og_url":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/","og_site_name":"Think Academy Canada Blog","article_published_time":"2026-08-10T13:47:00+00:00","article_modified_time":"2026-08-10T13:47:01+00:00","og_image":[{"width":1448,"height":1086,"url":"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_28_56-PM-1.png","type":"image\/png"}],"author":"Think Academy","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Think Academy","Est. reading time":"12 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/","url":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/","name":"Acute Triangle and Obtuse Triangle: Definitions and Examples","isPartOf":{"@id":"https:\/\/blog-admin.thethinkacademy.com\/#website"},"primaryImageOfPage":{"@id":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/#primaryimage"},"image":{"@id":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/#primaryimage"},"thumbnailUrl":"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_28_56-PM-1.png","datePublished":"2026-08-10T13:47:00+00:00","dateModified":"2026-08-10T13:47:01+00:00","author":{"@id":"https:\/\/blog-admin.thethinkacademy.com\/#\/schema\/person\/5e5752520edd7febcc1056443eab8850"},"description":"An acute triangle and obtuse triangle guide \u2014 how to identify them, and practice problems including contest geometry.","breadcrumb":{"@id":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/#primaryimage","url":"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_28_56-PM-1.png","contentUrl":"https:\/\/blog-admin.thethinkacademy.com\/wp-content\/uploads\/2026\/08\/ChatGPT-Image-Aug-10-2026-02_28_56-PM-1.png","width":1448,"height":1086},{"@type":"BreadcrumbList","@id":"https:\/\/blog-admin.thethinkacademy.com\/blog\/2026\/08\/10\/acute-triangle-and-obtuse-triangle-guide\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/blog-admin.thethinkacademy.com\/"},{"@type":"ListItem","position":2,"name":"Acute and Obtuse Triangles Explained: Definitions, Properties and Examples"}]},{"@type":"WebSite","@id":"https:\/\/blog-admin.thethinkacademy.com\/#website","url":"https:\/\/blog-admin.thethinkacademy.com\/","name":"Think Academy Canada Blog","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/blog-admin.thethinkacademy.com\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/blog-admin.thethinkacademy.com\/#\/schema\/person\/5e5752520edd7febcc1056443eab8850","name":"Think Academy","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/blog-admin.thethinkacademy.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f79e3f7bff09863820040f04b26b5731542ae3733cf505c30733842df6e7ff82?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f79e3f7bff09863820040f04b26b5731542ae3733cf505c30733842df6e7ff82?s=96&d=mm&r=g","caption":"Think Academy"},"sameAs":["https:\/\/blog-admin.thethinkacademy.com"],"url":"https:\/\/blog-admin.thethinkacademy.com\/blog\/author\/thinkacademy\/"}]}},"yoast_meta_description":"An acute triangle and obtuse triangle guide \u2014 how to identify them, and practice problems including contest geometry.","yoast_focus_keyword":"acute triangle and obtuse triangle","yoast_seo_title":"Acute Triangle and Obtuse Triangle: Definitions and Examples","_links":{"self":[{"href":"https:\/\/blog-admin.thethinkacademy.com\/wp-json\/wp\/v2\/posts\/65382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog-admin.thethinkacademy.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog-admin.thethinkacademy.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog-admin.thethinkacademy.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog-admin.thethinkacademy.com\/wp-json\/wp\/v2\/comments?post=65382"}],"version-history":[{"count":1,"href":"https:\/\/blog-admin.thethinkacademy.com\/wp-json\/wp\/v2\/posts\/65382\/revisions"}],"predecessor-version":[{"id":65387,"href":"https:\/\/blog-admin.thethinkacademy.com\/wp-json\/wp\/v2\/posts\/65382\/revisions\/65387"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blog-admin.thethinkacademy.com\/wp-json\/wp\/v2\/media\/65383"}],"wp:attachment":[{"href":"https:\/\/blog-admin.thethinkacademy.com\/wp-json\/wp\/v2\/media?parent=65382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog-admin.thethinkacademy.com\/wp-json\/wp\/v2\/categories?post=65382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog-admin.thethinkacademy.com\/wp-json\/wp\/v2\/tags?post=65382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}