Answer: To show that △WZY ≅ △YXW, we need to show that they are congruent by proving that all corresponding sides and angles are equal.
Given:
WZ⊥ZY and WX⊥XY, which implies ∠WZY = ∠YXW = 90°
∠ZYW ≅ ∠XWY (given)
WX ≅ ZY and WZ ≅ XY (given)
To prove:
△WZY ≅ △YXW
Proof:
By the given information, ∠WZY = ∠YXW = 90°.
By the given information, ∠ZYW ≅ ∠XWY.
Therefore, ∠WZY + ∠ZYW ≅ ∠YXW + ∠XWY. Combining these angles gives us ∠WZY + ∠ZYW = ∠YXW + ∠XWY.
Since the sum of interior angles in a triangle is 180°, we have:
∠WZY + ∠ZYW + ∠YZW = 180° for △WZY
∠YXW + ∠XWY + ∠YWX = 180° for △YXW
Substituting in the angle congruence (∠ZYW ≅ ∠XWY), we have:
∠WZY + ∠XWY + ∠YZW = 180° for △WZY
∠YXW + ∠ZYW + ∠YWX = 180° for △YXW
By the given information, WX ≅ ZY and WZ ≅ XY.
Therefore, by the Side-Angle-Side (SAS) congruence postulate, △WZY ≅ △YXW.
Hence, we have proved that △WZY ≅ △YXW.
Explanation: