{"id":836496,"date":"2024-07-13T12:36:55","date_gmt":"2024-07-13T07:06:55","guid":{"rendered":"https:\/\/leverageedu.com\/discover\/?p=836496"},"modified":"2024-07-13T12:36:55","modified_gmt":"2024-07-13T07:06:55","slug":"exam-prep-properties-of-triangle","status":"publish","type":"post","link":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-triangle\/","title":{"rendered":"Properties of Triangle: A Complete Guide"},"content":{"rendered":"\n<p>Triangles are fascinating and fundamental shapes in geometry, forming the basis for much of the subject. This guide will take you through the various properties of triangles, such as their types based on sides and angles, the sum of their interior angles, and important concepts like the Pythagorean theorem. Whether you&#8217;re a student just starting out or someone needing a refresher, this comprehensive guide to the properties of triangles will help you understand and appreciate the unique characteristics of triangles. Keep reading learn more about the properties of triangles and explore their formulas in a simple and straightforward way.<\/p>\n\n\n\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-definition-of-triangle\">Definition of Triangle<\/h2>\n\n\n\n<p>A triangle is a three-sided polygon with three edges and three vertices. It is one of the simplest shapes in geometry and is defined by its three sides and the angles between those sides. Here are some key properties of triangles.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXcuSKRIX5yyuJWS5d6iqpY4mfWuw1NvEBO0sMlHL2usaqjM18iJ0FJymNCsa5Ss2qjS3HYlhJD96EeFn9eD764Y0foyXDKsYcssWyOIvF09jqPO_H2n94dlS3sy50N3rwQZhCuJLNiu0fb1LhtF-VFeQW23?key=LpoiYGLruRSidt_8ra0Ahg\" ><\/figure>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Sum of Interior Angles<\/strong>: The sum of the interior angles of a triangle is always 180 degrees.<\/li>\n\n\n\n<li><strong>Types of Triangles by Sides<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Equilateral Triangle<\/strong>: All three sides are equal, and all three interior angles are 60 degrees.<\/li>\n\n\n\n<li><strong>Isosceles Triangle<\/strong>: Two sides are equal, and the angles opposite these sides are equal.<\/li>\n\n\n\n<li><strong>Scalene Triangle<\/strong>: All three sides are of different lengths, and all three interior angles are different.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n<li><strong>Types of Triangles by Angles<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Acute Triangle<\/strong>: All three interior angles are less than 90 degrees.<\/li>\n\n\n\n<li><strong>Right Triangle<\/strong>: One interior angle is exactly 90 degrees.<\/li>\n\n\n\n<li><strong>Obtuse Triangle<\/strong>: One interior angle is more than 90 degrees.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n<li><strong>Exterior Angles<\/strong>: The sum of the exterior angles of a triangle is always 360 degrees.<\/li>\n\n\n\n<li><strong>Perimeter<\/strong>: The perimeter of a triangle is the sum of the lengths of its three sides.<\/li>\n\n\n\n<li><strong>Area<\/strong>: The area of a triangle can be calculated using various formulas, such as <strong>1\/2 x base x height<\/strong> or Heron&#8217;s formula for more complex cases.<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-center has-electric-grass-gradient-background has-background has-medium-font-size\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-find-the-area-of-the-shaded-region\/\"><strong>Find the Area of the Shaded Region: Square, Rectangle<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-types-of-triangle\">Types of Triangle<\/h2>\n\n\n\n<p>Triangles can be categorized based on their sides and their angles. Here are the different types of triangles in each category.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXeGBz8o4RvPUMjU5PKaJ5bWelEHhU1YEBb3aAEn7GDjlRs_BCm58nNiZLXRFDPMbdrIWM7tW8WZRbt-N6EtnwahJe9MLXH24RRm3CIz_AWws0rn7M1MLEoH5JldcULlFQMU3GowLIDr13skkCSIN-3vTVxB?key=LpoiYGLruRSidt_8ra0Ahg\" ><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-types-of-triangles-by-sides\">Types of Triangles by Sides<\/h3>\n\n\n\n<p><strong>Equilateral Triangle<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXeuTaf0G2ZaklEZgmvxj7A6mITEqPxctExTCsGV-ohtaI9Q9TV_fTia9IZz8p99dOndPRgOw5hxReWZolgUTz32vWTQUFDL2E3UCn-bRj-7XSZ1gC9gPeGhgIx1Q-d-OmBR4pPi9y0G4ImJHiuMuXwSYAUK?key=LpoiYGLruRSidt_8ra0Ahg\" ><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>All three sides are of equal length.<\/li>\n\n\n\n<li>All three interior angles are equal, each measuring 60 degrees.<\/li>\n<\/ul>\n\n\n\n<p><strong>Isosceles Triangle<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXcWoIvr1SvRR1s4wMugldKuCro26iC8lBeWvXivySoSM-1SJx_mt6zgdNubzhJ7d5VGMedN01_6rA6lsTcVj3JkMVAGdLcDbHjoXz0-1A9yUb_YPMdxyyAqNc6tK7Iwg1rV7coZVTOIqiCX2525Kj9rQ8ZW?key=LpoiYGLruRSidt_8ra0Ahg\" ><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Two sides are of equal length.<\/li>\n\n\n\n<li>The angles opposite the equal sides are also equal.<\/li>\n<\/ul>\n\n\n\n<p><strong>Scalene Triangle<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXfDPLDJDl_Tyf9Lns2ArxEt5qSe8nygxW7lw6eaon_aDATG-YnqFd8GGgX9F22rt7lAoIU3VkY3IeN5lHq0Wa_C5ona4qW2AlvKxm2tyPHABqMNyAbkVLOdNlBy26nEDrZHhmKhKnv1oWLUyHiHawwXmd4o?key=LpoiYGLruRSidt_8ra0Ahg\" ><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>All three sides are of different lengths.<\/li>\n\n\n\n<li>All three interior angles are different.<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-types-of-triangles-by-angles\">Types of Triangles by Angles<\/h3>\n\n\n\n<p><strong>Acute Triangle<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXdUUlRrguguQsGlZ7izoPSS-2w6bcNZ-nuE2f0_efhQuDbBc3JE4sKiXanb6Nqido4axYa1xJjMz44Yz9dFn9mkBH6sbV4-EbdbtoczqVhzywnHafgHOq060M2PJ51vuZ_j9O4O7cOzPOj67iVZCYVn01g?key=LpoiYGLruRSidt_8ra0Ahg\" ><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>All three interior angles are less than 90 degrees.<\/li>\n<\/ul>\n\n\n\n<p><strong>Right Triangle<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXfUQrNm9JqQiyjy2w1iEQrXDUbUdpzIXDHGGx8hvGxov3GkuOXIHWeLRlLOZqmOD2LCWd5PZQiOatPGqaRGnsC_u8bOioa_9QejbdYRUoKzRxQ-lBHpex8EB3Y9gGLPqgXlDt-zcItfjfojcyUCe9g0fIg?key=LpoiYGLruRSidt_8ra0Ahg\" ><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One interior angle is exactly 90 degrees.<\/li>\n\n\n\n<li>The side opposite the right angle is called the hypotenuse, and it is the longest side of the triangle.<\/li>\n<\/ul>\n\n\n\n<p><strong>Obtuse Triangle<\/strong>:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img  decoding=\"async\"  src=\"data:image\/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAEAAAABAQMAAAAl21bKAAAAA1BMVEUAAP+KeNJXAAAAAXRSTlMAQObYZgAAAAlwSFlzAAAOxAAADsQBlSsOGwAAAApJREFUCNdjYAAAAAIAAeIhvDMAAAAASUVORK5CYII=\"  alt=\"\"  class=\" pk-lazyload\"  data-pk-sizes=\"auto\"  data-pk-src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXfIIZ583Qh2nuUQxKusPtv0Gmy0H6vmRv9jvs3IzCApP7BjGS9Hut6iTeMYfikKmiVxwufTwt8vO2MGJxZ0YWNIeFh7nmsekzhSioj2YbRHKEjCYtgNPImrPEhH9KUVwQKinnWa66lzxhs7wIuOfeJd7vvw?key=LpoiYGLruRSidt_8ra0Ahg\" ><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One interior angle is more than 90 degrees.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>Type by Sides<\/strong><\/td><td><strong>Description<\/strong><\/td><td><strong>Type by Angles<\/strong><\/td><td><strong>Description<\/strong><\/td><\/tr><tr><td><strong>Equilateral<\/strong><\/td><td>All sides and angles are equal<\/td><td><strong>Acute<\/strong><\/td><td>All angles are less than 90 degrees<\/td><\/tr><tr><td><strong>Isosceles<\/strong><\/td><td>Two sides and two angles are equal<\/td><td><strong>Right<\/strong><\/td><td>One angle is exactly 90 degrees<\/td><\/tr><tr><td><strong>Scalene<\/strong><\/td><td>All sides and angles are different<\/td><td><strong>Obtuse<\/strong><\/td><td>One angle is greater than 90 degrees<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-properties-of-triangle-with-formulas\">Properties of Triangle with Formulas<\/h2>\n\n\n\n<p>Triangles have various properties and associated formulas that help in solving geometric problems. Here\u2019s a detailed look at the properties of triangles along with their relevant formulas.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-1-sum-of-interior-angles\"><strong>1. Sum of Interior Angles<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Property<\/strong>: The sum of the interior angles of a triangle is always 180 degrees.<\/li>\n\n\n\n<li><strong>Formula<\/strong>: \u2220A+\u2220B+\u2220C=180\u2218<\/li>\n<\/ul>\n\n\n\n<p><strong>2. Sum of Exterior Angles<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Property<\/strong>: The sum of the exterior angles of a triangle is always 360 degrees.<\/li>\n\n\n\n<li><strong>Formula<\/strong>: \u2220D+\u2220E+\u2220F=360\u2218<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-3-types-of-triangles-based-on-angles-and-sides\"><strong>3. Types of Triangles Based on Angles and Sides<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Equilateral Triangle<\/strong>:\n<ul class=\"wp-block-list\">\n<li>All sides are equal.<\/li>\n\n\n\n<li>All angles are equal to 60 degrees.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Isosceles Triangle<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Two sides are equal.<\/li>\n\n\n\n<li>The angles opposite the equal sides are equal.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Scalene Triangle<\/strong>:\n<ul class=\"wp-block-list\">\n<li>All sides and angles are different.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Right Triangle<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Has one 90-degree angle.<\/li>\n\n\n\n<li>The side opposite the right angle is called the hypotenuse.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-4-perimeter-of-a-triangle\"><strong>4. Perimeter of a Triangle<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Property<\/strong>: The perimeter is the sum of the lengths of all three sides.<\/li>\n\n\n\n<li><strong>Formula<\/strong>: P=a+b+c.\n<ul class=\"wp-block-list\">\n<li>Where a,b, and c are the lengths of the sides.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-5-area-of-a-triangle\"><strong>5. Area of a Triangle<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Property<\/strong>: The area can be calculated using different methods depending on the information available.<\/li>\n\n\n\n<li><strong>Formula (Base and Height)<\/strong>: Area=1\/2\u00d7base\u00d7height<\/li>\n\n\n\n<li><strong>Heron&#8217;s Formula<\/strong>:\n<ul class=\"wp-block-list\">\n<li>Used when the lengths of all three sides are known.<\/li>\n\n\n\n<li>s=a+b+c\/2\u200b (semi-perimeter)<\/li>\n\n\n\n<li>Area= \u221a({s(s-a)(s-b)(s-c)}<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-6-pythagorean-theorem\"><strong>6. Pythagorean Theorem<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Property<\/strong>: Applies to right triangles.<\/li>\n\n\n\n<li><strong>Formula<\/strong>: c\u00b2=a\u00b2+b\u00b2\n<ul class=\"wp-block-list\">\n<li>Where ccc is the hypotenuse and aaa and bbb are the other two sides.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"h-7-altitude-median-and-angle-bisector\"><strong>7. Altitude, Median, and Angle Bisector<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Altitude<\/strong>:\n<ul class=\"wp-block-list\">\n<li>A perpendicular segment from a vertex to the line containing the opposite side.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Median<\/strong>:\n<ul class=\"wp-block-list\">\n<li>A segment connecting a vertex to the midpoint of the opposite side.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Angle Bisector<\/strong>:\n<ul class=\"wp-block-list\">\n<li>A segment that divides an angle into two equal parts.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><strong>Property<\/strong><\/td><td><strong>Description<\/strong><\/td><td><strong>Formula<\/strong><\/td><\/tr><tr><td>Sum of Interior Angles<\/td><td>Sum of all interior angles is 180 degrees<\/td><td><strong>\u2220A+\u2220B+\u2220C=180 degree<\/strong><\/td><\/tr><tr><td>Sum of Exterior Angles<\/td><td>Sum of all exterior angles is 360 degrees<\/td><td><strong>\u2220D+\u2220E+\u2220F=360 degree<\/strong><\/td><\/tr><tr><td>Perimeter<\/td><td>Sum of the lengths of all sides<\/td><td><strong>P = a+b+c<\/strong><\/td><\/tr><tr><td>Area (Base and Height)<\/td><td>Half the product of base and height<\/td><td><strong>Area=1\/2\u200b\u00d7base\u00d7height<\/strong><\/td><\/tr><tr><td>Area (Heron&#8217;s Formula)<\/td><td>Square root of product of semi-perimeter and differences<\/td><td><strong>Area= \u221a({s(s\u2212a)(s\u2212b)(s\u2212c)}<\/strong><\/td><\/tr><tr><td>Pythagorean Theorem (Right Triangle)<\/td><td>Hypotenuse squared equals sum of squares of other sides<\/td><td><strong>c\u00b2 = a\u00b2+b\u00b2<\/strong><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-properties-of-triangle-solved-examples\">Properties of Triangle Solved Examples<\/h2>\n\n\n\n<p>Here are 10 solved examples related to different properties and formulas of triangles.<\/p>\n\n\n\n<p><strong>Q1<\/strong>: <strong>Given a triangle with angles \u2220A=50\u2218 and \u2220B=60\u2218, find \u2220C.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p>\u2220A+\u2220B+\u2220C=180\u2218<\/p>\n\n\n\n<p>50\u2218+60\u2218+\u2220C=180\u2218<\/p>\n\n\n\n<p>\u2220C=180\u2218\u2212110\u2218=70\u2218<\/p>\n\n\n\n<p><strong>Q2: Find the perimeter of a triangle with sides a=5\u2009cm, b=7\u2009cm, and c=10cm.<\/strong><\/p>\n\n\n\n<p><strong>Solution: <\/strong>P=a+b+c<\/p>\n\n\n\n<p>=5cm+7cm+10cm<\/p>\n\n\n\n<p>=22cm<\/p>\n\n\n\n<p><strong>Q3: Calculate the area of a triangle with a base of 8\u2009cm and height of 5\u2009cm.&nbsp;<\/strong><\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p>Area=1\/2\u00d7base\u00d7height<\/p>\n\n\n\n<p>=1\/2\u00d78\u2009cm\u00d75\u2009cm=20\u2009cm<\/p>\n\n\n\n<p>Area=1\/2\u200b\u00d7base\u00d7height<\/p>\n\n\n\n<p>=1\/2\u200b\u00d78cm\u00d75cm=20cm\u00b2<\/p>\n\n\n\n<p><strong>Q4<\/strong>: Find the area of a triangle with sides a=6\u2009cm, b=8\u2009cm, and c=10\u2009c.&nbsp;<\/p>\n\n\n\n<p><strong>Solution<\/strong>: s=2a+b+c\u200b=26+8+10\u200b=12<\/p>\n\n\n\n<p><strong>Area= \u221a({s(s\u2212a)(s\u2212b)(s\u2212c)}<\/strong><\/p>\n\n\n\n<p>\u221a12(12-6)(12-8)(12-10)<\/p>\n\n\n\n<p>=\u221a12x6x4x2<\/p>\n\n\n\n<p>=\u221a576<\/p>\n\n\n\n<p>=24cm\u00b2<\/p>\n\n\n\n<p><strong>Q5<\/strong>: In a right triangle, if a=3\u2009cm and b=4\u2009cm, find the hypotenuse c.&nbsp;<\/p>\n\n\n\n<p><strong>Solution<\/strong>:<\/p>\n\n\n\n<p><strong>c\u00b2 = a\u00b2+b\u00b2<\/strong><\/p>\n\n\n\n<p>=3<strong>\u00b2<\/strong>+4<strong>\u00b2<\/strong><\/p>\n\n\n\n<p>=9+16<\/p>\n\n\n\n<p>=\u221a25<\/p>\n\n\n\n<p>=5cm<\/p>\n\n\n\n<p><strong>Q6<\/strong>: What is the measure of each angle in an equilateral triangle?&nbsp;<\/p>\n\n\n\n<p><strong>Solution<\/strong>: In an equilateral triangle, all angles are equal.<\/p>\n\n\n\n<p>\u2220A=\u2220B=\u2220C=60\u2218<\/p>\n\n\n\n<p><strong>Q7<\/strong>: Find the sum of the exterior angles of any triangle.&nbsp;<\/p>\n\n\n\n<p><strong>Solution<\/strong>: The sum of the exterior angles of any triangle is always 360\u2218.<\/p>\n\n\n\n<p><strong>Q8<\/strong>: Find the altitude of an equilateral triangle with side length a=6\u2009cm.&nbsp;<\/p>\n\n\n\n<p><strong>Solution<\/strong>: Altitude= \u221a3\/2 x a<\/p>\n\n\n\n<p>= \u221a3\/2 x 6cm<\/p>\n\n\n\n<p>=3\u221a3 cm<\/p>\n\n\n\n<p><strong>Q9<\/strong>: In a right triangle, if the hypotenuse c=13\u2009cm and one side a=5\u2009cm, find the other side b.&nbsp;<\/p>\n\n\n\n<p><strong>Solution<\/strong>: <strong>c\u00b2 = a\u00b2+b\u00b2<\/strong><\/p>\n\n\n\n<p>= 13\u00b2 = 5\u00b2 + b\u00b2<\/p>\n\n\n\n<p>=169 = 25 + b\u00b2<\/p>\n\n\n\n<p>= b\u00b2 =144<\/p>\n\n\n\n<p>= b = \u221a144<\/p>\n\n\n\n<p>=12cm<\/p>\n\n\n\n<p><strong>Q10<\/strong>: Given an isosceles triangle with equal sides a=5\u2009cm and base b=6\u2009cm, find the perimeter and area.<\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p><strong>Perimeter:<\/strong><\/p>\n\n\n\n<p>P=2a+b<\/p>\n\n\n\n<p>=2\u00d75\u2009cm+6\u2009cm<\/p>\n\n\n\n<p>=16\u2009cm<\/p>\n\n\n\n<p><strong>Area<\/strong>:<\/p>\n\n\n\n<p>Height = \u221a a\u00b2 &#8211; (b\/2)\u00b2<\/p>\n\n\n\n<p>= \u221a5\u00b2 &#8211; 3\u00b2<\/p>\n\n\n\n<p>=\u221a25-9<\/p>\n\n\n\n<p>=\u221a16 = 4cm<\/p>\n\n\n\n<p>Area=1\/2\u200b\u00d7b\u00d7height<\/p>\n\n\n\n<p>=1\/2\u200b\u00d76cm\u00d74cm<\/p>\n\n\n\n<p>=12cm<\/p>\n\n\n\n<p class=\"has-text-align-center has-electric-grass-gradient-background has-background has-medium-font-size\"><strong>Also Read: <\/strong><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-formula-of-profit-and-loss\/\"><strong>Formula of Profit and Loss: Percentages<\/strong><\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-faqs\">FAQs<\/h2>\n\n\n\n<div class=\"schema-faq wp-block-yoast-faq-block\"><div class=\"schema-faq-section\" id=\"faq-question-1720853994188\"><strong class=\"schema-faq-question\">What is the triangle property?<\/strong> <p class=\"schema-faq-answer\">The sum of all the angles in any triangle is 180\u00b0.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1720854004654\"><strong class=\"schema-faq-question\"><strong>What is the triangle theorem?<\/strong><\/strong> <p class=\"schema-faq-answer\">First, all three of the inside sides of a triangle add up to 180 degrees. We know that if ABC is a triangle, then \u2220A + \u2220B + \u2220C = 180\u00b0. 2. The angles at the base of an isosceles triangle are the same.<\/p> <\/div> <div class=\"schema-faq-section\" id=\"faq-question-1720854018964\"><strong class=\"schema-faq-question\"><strong>What is a reflex angle?<\/strong><\/strong> <p class=\"schema-faq-answer\">An angle that is between 180 and 360 degrees is called a reflex angle. Like, 270 degrees is an example of a reflex angle. An acute angle is less than 180 degrees, an obtuse angle is more than 180 degrees, and a right angle is above 180 degrees.<\/p> <\/div> <\/div>\n\n\n\n<p class=\"has-text-align-center has-vivid-red-color has-text-color has-link-color has-medium-font-size wp-elements-adc4b1619be72b19c4386dda21667032\"><strong>RELATED BLOGS<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-table is-style-stripes\"><table><tbody><tr><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-faces-edges-and-vertices\/\"><strong>What are Vertices, Faces And Edges?<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-perimeter-of-rectangle\/\"><strong>Perimeter of Rectangle: Formula and Examples\u00a0<\/strong><\/a><br><\/td><\/tr><tr><td><a href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/study-material\/maths\/basic-concepts-surface-area-of-prism\/\"><strong>Surface Area of Prism: Formula and Steps<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-area-of-rectangle\/\"><strong>Area of Rectangle: Formula and Example\u00a0<\/strong><\/a><br><\/td><\/tr><tr><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-surface-area-of-a-cuboid\/\"><strong>Surface Area of a Cuboid: Definition, Derivation and Formula<\/strong><\/a><\/td><td><a href=\"https:\/\/leverageedu.com\/discover\/school-education\/basic-concepts-maths-shapes\/\"><strong>Different Maths Shapes for Students and Kids<\/strong><\/a><br><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>This was all about \u201c<strong>Properties of Triangle<\/strong>\u201d. For more such informative blogs, check out our<a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/study-material\/\"> Study Material Section<\/a>, or you can learn more about us by visiting our<a href=\"https:\/\/leverageedu.com\/discover\/category\/indian-exams\/\">&nbsp; Indian exams<\/a> page.<\/p>\n","protected":false},"excerpt":{"rendered":"Triangles are fascinating and fundamental shapes in geometry, forming the basis for much of the subject. This guide&hellip;\n","protected":false},"author":115,"featured_media":836501,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"editor_notices":[],"footnotes":""},"categories":[369,476,396],"tags":[],"class_list":{"0":"post-836496","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-indian-exams","8":"category-maths","9":"category-study-material"},"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.3) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Properties of Triangle: A Complete Guide - Leverage Edu Discover<\/title>\n<meta name=\"description\" content=\"Read this article on Properties of Triangle.Learn more about properties of triangle in detail.Let&#039;s start !\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-triangle\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Properties of Triangle: A Complete Guide\" \/>\n<meta property=\"og:description\" content=\"Read this article on Properties of Triangle.Learn more about properties of triangle in detail.Let&#039;s start !\" \/>\n<meta property=\"og:url\" content=\"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-triangle\/\" \/>\n<meta property=\"og:site_name\" content=\"Leverage Edu Discover\" \/>\n<meta property=\"article:published_time\" content=\"2024-07-13T07:06:55+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/blogassets.leverageedu.com\/media\/uploads\/sites\/9\/2024\/07\/15073736\/Properties-of-Triangle-2.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"1024\" \/>\n\t<meta property=\"og:image:height\" content=\"640\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"Mohit Rajak\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Mohit Rajak\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"Properties of Triangle: A Complete Guide - 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I find peace and purpose in crafting verses that dance between the lines of poetry. With my pen as my wand, I weave intricate tales and heartfelt musings, breathing life into the blank canvas of each page. Blogging is my window to the world way of sharing thoughts, emotions, and a perspective uniquely my own. Every word I write is a brushstroke in the ever-evolving painting of my literary journey.","sameAs":["https:\/\/www.instagram.com\/xx_a.m.strings_xiv\/","https:\/\/www.linkedin.com\/in\/mohit-rajak-a9a5a2162\/"],"url":"https:\/\/leverageedu.com\/discover\/author\/mohit\/"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-triangle\/#faq-question-1720853994188","position":1,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-triangle\/#faq-question-1720853994188","name":"What is the triangle property?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"The sum of all the angles in any triangle is 180\u00b0.","inLanguage":"en-US"},"inLanguage":"en-US"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-triangle\/#faq-question-1720854004654","position":2,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-triangle\/#faq-question-1720854004654","name":"What is the triangle theorem?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"First, all three of the inside sides of a triangle add up to 180 degrees. We know that if ABC is a triangle, then \u2220A + \u2220B + \u2220C = 180\u00b0. 2. The angles at the base of an isosceles triangle are the same.","inLanguage":"en-US"},"inLanguage":"en-US"},{"@type":"Question","@id":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-triangle\/#faq-question-1720854018964","position":3,"url":"https:\/\/leverageedu.com\/discover\/indian-exams\/exam-prep-properties-of-triangle\/#faq-question-1720854018964","name":"What is a reflex angle?","answerCount":1,"acceptedAnswer":{"@type":"Answer","text":"An angle that is between 180 and 360 degrees is called a reflex angle. Like, 270 degrees is an example of a reflex angle. An acute angle is less than 180 degrees, an obtuse angle is more than 180 degrees, and a right angle is above 180 degrees.","inLanguage":"en-US"},"inLanguage":"en-US"}]}},"acf":[],"_links":{"self":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/836496","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/users\/115"}],"replies":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/comments?post=836496"}],"version-history":[{"count":0,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/posts\/836496\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media\/836501"}],"wp:attachment":[{"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/media?parent=836496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/categories?post=836496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/leverageedu.com\/discover\/wp-json\/wp\/v2\/tags?post=836496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}