Question

In triangle xyz, if angle x is 90° and angle y is 30°, and in triangle tuv, angle u is 30° and angle v is 60°, which statement is true about the two triangles?

1) Triangle xyz is congruent to triangle tuv
2) Triangle xyz is congruent to triangle vut
3) No congruency statement can be made because only two angles in each triangle are known
4) No congruency statement can be made because the side lengths are unknown

Answer 1

Triangle XYZ is congruent to triangle TUV.

Step-by-step explanation:

Based on the given information, we can determine the third angle of triangle XYZ by subtracting the sum of angles X and Y from 180 degrees. Angle Z = 180 - 90 - 30 = 60 degrees.

Now, let's compare the angles of triangle XYZ with the angles of triangle TUV. Angle U is 30 degrees, which is equal to angle Y in triangle XYZ. Angle V is 60 degrees, which is equal to angle Z in triangle XYZ.

Since all three angles of triangle XYZ are equal to the corresponding angles of triangle TUV, we can conclude that the two triangles are congruent.