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Identify the proof to show that △WZY≅△YXW , where WZ⊥ZY , WX⊥XY , ∠ZYW≅∠XWY , WX≅ZY , and WZ≅XY

User Kuzgun
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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:

User Isuru Amarathunga
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