Question

given: ∠v = ∠y, wz is the perpendicular bisector of vy. can you use the asa postulate or the aas theorem to prove the triangles congruent? neither apply both apply by asa only by aas only

Explanation:

Step1: Recall ASA and AAS criteria

ASA (Angle - Side - Angle) requires two angles and the included side to be congruent. AAS (Angle - Angle - Side) requires two angles and a non - included side to be congruent.

Step2: Analyze given information

We know that $\angle V=\angle Y$ and $\overline{WZ}$ is the perpendicular bisector of $\overline{VY}$, so $\angle WZV=\angle WZY = 90^{\circ}$ and $VZ = ZY$. Also, $\overline{WZ}$ is common to both $\triangle WZV$ and $\triangle WZY$.

Step3: Check ASA

We have $\angle V=\angle Y$, $\overline{WZ}$ is common, and $\angle WZV=\angle WZY$. So, we have two angles and the included side congruent, which satisfies ASA.

Step4: Check AAS

We have $\angle V=\angle Y$, $\angle WZV=\angle WZY$, and $\overline{WZ}$ (non - included side with respect to the pairs of angles) is common. So, it also satisfies AAS.

Answer:

both apply