SOLUTION: I am trying to prove triangles similar. The bigger triangle has an angle measuring 30 degrees and the two longer sides are congruent. The smaller triangles has an angle measure of
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Question 181611: I am trying to prove triangles similar. The bigger triangle has an angle measuring 30 degrees and the two longer sides are congruent. The smaller triangles has an angle measure of 70 degrees and he two longer sides are congruent. My question is that whether or not I can prove them similar, and if so what postulate or theorem can I use? Answer by solver91311(24713) (Show Source):
Two congruent sides means that the triangle is isoceles and therefore also has two congruent angles. So, for your larger triangle, you must have a 30 degree angle and two 75 degree angles because the sum of the interior angles must be 180. (two 30 degree angles and a 120 degree angle is impossible because you said the longer sides are congruent). For the smaller triangle, you must have two 70 degree angles and a 40 degree angle (again two 40s and a 70 not possible because the longer sides are congruent). The angle measures in the two triangles are not equal, therefore the triangles are not similar.
