Question

In ΔXYZ, m∠X = 90° and m∠Y = 30°. In ΔTUV, m∠U = 30° and m∠V = 60°. Which is true about the two triangles?

Answer 1

The best option is A. Both are right triangles.

Answer 2

Answer: C. No congruency statement can be made because the side lengths are unknown.

Step-by-step explanation:

Given: In ΔXYZ, m∠X = 90° and m∠Y = 30°. In ΔTUV, m∠U = 30° and m∠V = 60°.

By using angle sum property in ΔXYZ, we get

m∠X+m∠Y+m∠Z = 180°

⇒90° +30°+m∠Z = 180°

⇒m∠Z = 180°-120°

⇒m∠Z = 60°

Now, in  ΔXYZ and ΔTUV

m∠Y =m∠U =30° and m∠Z = m∠V = 60°

So by AA similarity both triangles are similar but not congruent because the side lengths are unknown to apply any congruent postulate of theorem.