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

Answer 1

Y=U
X=T
Z=V
A. ΔXYZ ≅ ΔTUV

Answer 2

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

Explanation:

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

In triangle TUV,

m∠T = 180° - ( m∠U +m∠V) =180° - ( 30° + 60°) = 90°

While in triangle XYZ,

m∠Z = 180° -( m∠X+m∠Y ) = 180° - ( 90° + 30°) = 60°

Hence, In the triangles XYZ and TUV,

∠ X ≅ ∠ T, ∠ Y ≅ ∠ U and ∠ Z ≅ ∠ V

Thus, By AAA similarity postulate,

Triangle XYX and TUV are similar,

Since, if two triangles are similar then they are congruent if there is at least one pair of corresponding congruent sides.

Thus, we can not prove these triangle congruent unless we have the side length.

Hence, No congruency statement can be made because the side lengths are unknown.