Problems on Congruenchttps:\/\/ccssanswers.com\/y of Triangles<\/a><\/li>\n<\/ul>\nProblems on Isosceles Triangle<\/h3>\n
Problem 1:<\/strong>
\nIf the two equal sides of an isosceles triangle are 3x – 1, 2x + 2. The third side is 2x. Find the value of x and the perimeter of the triangle.<\/p>\nSolution:<\/strong>
\nGiven that,
\nEqual sides of an isosceles triangle are 3x – 1, 2x + 2. So, equate them.
\n3x – 1 = 2x + 2
\n3x – 2x = 2 + 1
\nx = 3
\nThird side of an isosceles triangle is 2x
\nThird side = 2 x 3 = 6
\nFirst two sides are 3x – 1, 2x + 2
\n= 3(3) – 1, 2(3) + 2
\n= 9 – 1, 6 + 2
\n= 8, 8
\nPerimeter of the triangle = 8 + 8 + 3
\n= 19.
\nTherefore, the value of x is 3 units, perimeter of the triangle is 19 units.<\/p>\nProblem 2:<\/strong>
\nThe base BC of triangle ABC has produced both ways and the measure of exterior angles formed are 94\u00b0, 126\u00b0. Find \u2220BAC.<\/p>\nSolution:<\/strong>
\nGiven that,
\nBase = BC
\n\u2220ACD = 126\u00b0, \u2220ABE = 94\u00b0
\nWe know that,
\n\u2220ABE + \u2220ABC = 180\u00b0
\n\u2220ABC = 180\u00b0 – \u2220ABE = 180\u00b0 – 94\u00b0
\n= 86\u00b0
\nAgain, \u2220ACB + \u2220ACD = 180\u00b0
\n\u2220ACB = 180\u00b0 – \u2220ACD = 180\u00b0 – 126\u00b0
\n= 54\u00b0
\nIn \u0394ABC
\n\u2220ABC + \u2220ACB + \u2220BAC = 180\u00b0
\n86\u00b0 + 54\u00b0 + \u2220BAC = 180\u00b0
\n\u2220BAC = 180\u00b0 – 140\u00b0 = 40\u00b0<\/p>\nFreuently Asked Question’s<\/h3>\n
1. What are the rules of an isosceles triangle?<\/strong><\/p>\nIn an isosceles triangle, two sides are congruent, the third side is called the base. Two angles opposite to equal sides are congruent.<\/p>\n
2. What two angles are equal in an isosceles triangle?<\/strong><\/p>\nTwo sides are equal in the measure in an isosceles triangle called legs. The angles opposite to legs are also equal.<\/p>\n
3. What happens when equal sides of an isosceles triangle are produced?<\/strong><\/p>\nIf the equal sides of an isosceles triangle are produced, then the exterior angles are equal and obtuse.<\/p>\n
4. What are the 3 properties of an isosceles triangle?<\/strong><\/p>\n\n- It has two sides of equal length.<\/li>\n
- The angles opposite to equal sides are equal in measure.<\/li>\n
- The altitude from one vertex to the base is the perpendicular bisector of the base.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"
An isosceles triangle is a special kind of triangle that has two sides of equal length, no matter in what direction the peak of the triangle points. The important properties of an isosceles triangle are it has two equal sides, two equal angles (base angles). According to the isosceles triangle theorem if equal sides of … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143303"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=143303"}],"version-history":[{"count":2,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143303\/revisions"}],"predecessor-version":[{"id":143306,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143303\/revisions\/143306"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=143303"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=143303"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=143303"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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