Question

Use complete sentences to describe the similarity between the three triangles shown in the diagram below.

Answer 1

The 3 triangles are similar - because  all 3 angles are equal. Note that all the lines are also parallel because of the 3 equal angles. They all have the same shape.

Answer 2

Answer:

These three triangles are similar triangles because their corresponding angles are congruent.

Step-by-step explanation:

Two triangles are called similar triangles if their corresponding sides are proportional or all corresponding interior angles are congruent (equal).

From the given figure it is noticed that the corresponding interior angles are congruent.

In triangle ABC, PQR and XYZ

$\angle A\cong \angle P\cong \angle X$

$\angle B\cong \angle Q\cong \angle Y$

$\angle C\cong \angle R\cong \angle Z$

So by AA rule of similarity, we get

$\triangle ABC\sim \triangle PQR\sim \triangle XYZ$

Therefore these three triangles are similar triangles because their corresponding angles are congruent.