Question

If ∠WXZ≅∠YXZ and WZ = 38, what is YZ?

Answer 1

Answer:  38

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Explanation:

The square markers tell us that we have right angles (aka 90 degree angles) at angle XYZ and XWZ. They are congruent by definition.

Another pair of congruent angles is WXZ and YXZ which are the left-most angles of each triangle.

The sides XZ and XZ are congruent to each other (reflexive property)

Based on those three previous paragraphs, we can use the Angle Angle Side (AAS) congruence theorem to prove that the triangles are congruent.

Specifically we could write $\triangle XYZ \cong \triangle XWZ$. The order of the letters is important so we know which letters pair up (eg: Y and W pair up as the 90 degree angles).

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In short, the triangles are identical copies of each other. The upper triangle reflects over the line XZ to get the lower triangle, and vice versa. This means the smaller corresponding pieces must also be the same.

In this case, WZ = YZ = 38