Question

Two Isosceles triangles have congruent vertex angles. Explain why the two triangles must be similar .

Answer 1

Two isosceles triangles with congruent vertex angles are similar because their angle measurements are the same.

Step-by-step explanation:

Two isosceles triangles have congruent vertex angles. This means that the measure of the vertex angles in both triangles is the same. Since the sum of the three angles in a triangle is always 180 degrees, the remaining two angles in each triangle must also be congruent. Therefore, the two triangles have the same angle measurements and are similar.

Answer 2

they are always similar because if the vertex of one is congruent to the vertex angle of another.

Step-by-step explanation:

let the congruent vertex angles have measure x. in any triangle the three angles have to add up to 180 so the base angle has to add up to 180-x in both triangles. in a isosceles triangle the base angles are congruent so each base angle has to measure (180-x)/2 in both triangles. therefore all three angle of the 2 triangles are congruent so the triangles must be similar by AA.