Question

Your friend uses the figure to say that all the exterior angles of any isosceles triangle are congruent. Is your friend correct? Explain your reasoning

Answer 1

No.

Explanation:

An isosceles triangle has two sides of equal length. Therefore, only two of its interior angles are congruent.

The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles). Therefore, as not all of the three interior angles of an isosceles triangle are congruent, all the exterior angles will also not be congruent.

Answer 2

• All the exterior angles of any isosceles triangle are congruent - FALSE statement

Explanation:

We know that the exterior angle of a triangle is the sum of remote interior angles.

If the triangle is equilateral then the sum of any two interior angles is same otherwise, with any isosceles triangle, we get different sums and therefore the friend is wrong.