Question

in △xyz, m∠x = 90° and m∠y = 30°. in △tuv, m∠u = 30° and m∠v = 60°. which is true about the two triangles? no congruency statement can be made because only two angles in each triangle are known. △xyz ≅ △tuv △xyz ≅ △vut no congruency statement can be made because the side lengths are unknown.

Explanation:

Step1: Recall congruence criteria

Congruence of triangles requires information about angles and side - lengths. Common criteria are SSS (Side - Side - Side), SAS (Side - Angle - Side), ASA (Angle - Side - Angle), AAS (Angle - Angle - Side) and HL (Hypotenuse - Leg for right - angled triangles).

Step2: Analyze given information

In \(\triangle XYZ\), \(m\angle X = 90^{\circ}\) and \(m\angle Y=30^{\circ}\), and in \(\triangle TUV\), \(m\angle U = 30^{\circ}\) and \(m\angle V = 60^{\circ}\). We only know the measures of two angles in each triangle. To prove congruence, we need at least one side - length information in addition to angle information.

Answer:

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