Question

Which postulate or theorem proves that these two triangles are congruent?

SAS Congruence Postulate
HL Congruence Theorem
AAS Congruence Theorem
ASA Congruence Postulate

Answer 1

AAS Congruence Theorem

Explanation:

Answer 2

AAS Congruence Theorem

Explanation:

According to the problem,

`\angle Y \cong \angle X\\\angle XWZ \cong \angle YWZ\\WZ \cong WZ`

So, we know by defintion that all three internal angles must sum 180°,

`\angle XWZ + \angle X +\angle XZW = 180\°\\\angle YWZ + \angle Y +\angle YZW = 180\°`

Both sums are equal

`\angle XWZ + \angle X +\angle XZW = \angle YWZ + \angle Y +\angle YZW \\\angle XZW = \angle YZW`

As you can observe, we have all three correspoing angles equals, we could demonstrate the triangles congruence by AAA postulate, but it's not a choice.

The easiest form to demonstrate this congruence is using AAS congruence theorem, which state if two pair of corresponding angles are congruent, and one pair of corresponding sides is congruent, then those triangles are congruent. And we have since the beginning two angles and one side all congruents.

Therefore, we can demonstrate it with AAS Congruence Theorem.