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Isosceles Triangles Base Angles Theorem If two sides of a triangle are congruent, then the base angles are also congruent. Base angles are the angles at the ends of the 2 congruent segments. So, in the diagram angles B and C are congruent. Base angle Base angle Converse of base angles theorem If two angles in a triangle are congruent, then the triangle is an isosceles triangle. That means that the 2 sides of the triangles are also congruent. This is an isosceles triangle, so the 2 sides are congruent… 5x + 5 = 35 5x = 30 x =6 Find the value of x This is an isosceles triangle, so the 2 angles are congruent… 9x = 72 x=8 Find the value of x x + x + 102 = 180 2x + 102 = 180 2x = 78 x = 39 Find the value of x The sum of the interior x + 7 = 55 angles is 180… x = 48 55 + 55 + y = 180 110 + y = 180 y = 170 Now find y Find x and y x = 9y 9y = 45 y =5 hmmm…… 90 + x + x = 180 90 + 2x = 180 2x = 90 x = 45
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