Question

in $\triangle xyz$, $mangle x = 90^{circ}$ and $mangle y = 30^{circ}$. in $\triangle tuv$, $mangle u = 30^{circ}$ and $mangle v = 60^{circ}$. which is true about the two triangles? $\triangle xyzcong\triangle tuv$ $\triangle xyzcong\triangle vut$ no congruency statement can be made because only two angles in each triangle are known. no congruency statement can be made because the side lengths are unknown.

Explanation:

Step1: Recall triangle - congruence criteria

Triangle - congruence criteria (SSS, SAS, ASA, AAS, HL) require information about side - lengths or a combination of side - lengths and angles.

Step2: Analyze given information

In $\triangle XYZ$, we know $m\angle X = 90^{\circ}$ and $m\angle Y=30^{\circ}$. In $\triangle TUV$, we know $m\angle U = 30^{\circ}$ and $m\angle V = 60^{\circ}$. We only have angle - measure information and no information about side - lengths.

Answer:

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