Questions: Y is the midpoint of XZ and triangle VWY is equilateral. Complete the proof that angle Z is congruent to angle X.

Transcript text: $Y$ is the midpoint of $\overline{X Z}$ and $\triangle V W Y$ is equilateral. Complete the proof that $\angle Z \cong \angle X$.

Solution

Solution Steps

Step 1: Identify given information

We are given that Y is the midpoint of XZ, meaning XY = YZ. We are also given that triangle VWY is equilateral, meaning VW = WY = VY. Additionally, WX = WZ is marked on the diagram.

Step 2: Prove triangles congruent

We can see that triangles WXY and WZY are congruent by SSS. They share side WY, WX and WZ are congruent, and XY and YZ are congruent.

Step 3: Corresponding angles of congruent triangles are congruent.

Because triangles WXY and WZY are congruent, their corresponding angles are congruent. Therefore, angle X is congruent to angle Z.

Final Answer

∠X ≅ ∠Z Proven.

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