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?

A. ΔXYZ ≅ ΔVUT
B. No congruency statement can be made because only two angles in each triangle are 0known.
C. No congruency statement can be made because the side lengths are unknown.

Answer 1

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

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.

Answer 2

The best option is A. Both are right triangles.