Question

In XYZ, mX=90 and mY=30.In TUV,mU= 30 and mV=60. Which is true about the two triangles? XYZ=TUV, XYZ= 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 length are unknown.

Answer 1

Is:D

Explanation:

Answer 2

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

Explanation:

The sum of the measures of all interior angles in a triangle is always 180°.

In triangle XYZ,

`m\angle X=90^(\circ)\\ \\m\angle Y=30^(\circ),`

then

`m\angle X+m\angle Y+m\angle Z=180^(\circ)\Rightarrow m\angle Z=180^(\circ)-90^(\circ)-30^(\circ)=60^(\circ)`

In triangle TUV,

`m\angle U=30^(\circ)\\\\m\angle V=60^(\circ),`

then

`m\angle T+m\angle U+m\angle V=180^(\circ)\Rightarrow m\angle T=180^(\circ)-30^(\circ)-60^(\circ)=90^(\circ)`

We have two triangles with congruent angles but we have no information about side lengths. Therefore, can not be made because the side length are unknown. Correct option is last option.