Practice Exam

Question 17 • TPS EdX Geometry

Which best explains whether or not all isosceles triangles are similar?

Answer

All isosceles triangles are similar. The triangle sum theorem states that the sum of the angles in a triangle is 180 degrees . Therefore, the third angle can always be determined.

All isosceles triangles are not similar. The pair of congruent angles within one triangle is not necessarily congruent to the pair of congruent angles within the other triangle.

All isosceles triangles are similar. Two angles within each triangle are always congruent.

All isosceles triangles are not similar. Given only the vertex angle of an isosceles triangle, there is not enough information to determine the measures of the base angles. Therefore, it is not possible to determine if the base angles of one isosceles triangle are congruent to the base angles of another.

Explanation

For triangles to be similar, their corresponding angles must be equal. An isosceles triangle has two equal angles, but the measure of those angles can vary from one isosceles triangle to another. For example, triangles with angles 50°, 50°, 80° and 70°, 70°, 40° are both isosceles, but their angles do not match, so they are not similar. Thus, the pair of congruent angles in one triangle is not necessarily congruent to the pair in another.

AI-written and checked against the verified answer.

More from this Course

Practice Test

Practice Test

Test