Question

Look at the figure. Name the postulate or theorem you can use to prove the triangles congruent

Answer 1

They are congruent by AAS theorem.

Explanation:

From the figure, both triangle have a common side which is side VY.

Also, the figure is saying that angle YVW and angle ZVY are congruent. Additionally, angles YWV and VZY are congruent.

So, we have the congruence between two pairs corresponding sides and one pair of corresponding sides.

Therefore, we can deduct that
`\triangle VZY \cong \triangle VWY` by Angle-Angle-Side Theorem (AAS).

The AAS is not a postulate, is a theorem which is demonstrated from the initial postulates of congruence.

This means the right answer is the second choice.

Answer 2

B. AAS

Explanation:

The diagram shows two triangles ZVY and WVY.

In these triangles,

• ∠VZY ≅ ∠VWY - given;
• ∠ZVY ≅ ∠WVY - given;
• VY ≅ VY - Reflexive property of Equality

Thus, we have two pairs of congruent angles and a pair of not-included conruent sides.

AAS Postulate states that if two angles and the non-included side of one triangle are congruent to two angles and the non-included side of another triangle, then these two triangles are congruent.

So, we can use AAS Postulate.