In one isosceles triangle, the apex angle is 24 degrees, and in the other isosceles triangle, the base angle is 78

| September 7, 2021 | education

In one isosceles triangle, the apex angle is 24 degrees, and in the other isosceles triangle, the base angle is 78 degrees. Prove that triangles are similar.

The solution of the problem:
In the problem statement, two isosceles triangles are given, triangle ABC and triangle A1B1C1.
Consider a triangle ABC. In this triangle, the angle B at the apex is 24 degrees.
1. Find what is the sum of the angles of the triangle at the base.
180-24 = 156 degrees.
2. Find what each of the angles at the base of the triangle is equal to.
156/2 = 78 degrees.
Consider an isosceles triangle A1B1C1. At the base, the angle is A1 = C1 = 78 degrees.
1. Let’s find what is the angle B1 at the apex of the triangle.
180-78-78 = 24 degrees.
Answer: In these triangles, the angles are equal, and the sides of one triangle are proportional to the sides of the other triangle, which means that the triangles are similar.



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