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Maths-

General

Easy

Question

Prove that UZ = YZ

hint Hint:

Use the appropriate congruence rule.

The correct answer is: Hence proved

Complete step by step solution:
Consider 2 triangles, △XYZ and △WUZ
From the figure, we have
XZ = WZ (given)
∠XZY = ∠WZU (given)
∠XYZ = ∠WUZ (given)
By angle sum property,
Now, ∠YXZ = 180° - (∠XZY + ∠XYZ)
∠UWZ = 180° - (∠WZU + ∠WUZ) = 180° - (∠XZY + ∠XYZ)
⇒ ∠YXZ = ∠UWZ
So, In △ XYZ and △WUZ
∠YXZ = ∠UWZ (proved)
XZ = WZ (given)
∠XZY = ∠WZU (given)
So, △XYZ ⩭ △WUV by ASA congruence criterion
⇒ UZ = YZ(corresponding parts of congruent triangles)
Hence proved

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