Question

In triangle XYZ, angle xyz =90 °and XY =1/2 XZ Prove that angle YXZ =60 °

Answer 1

Answer:

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Answer 2

given:

ΔXYZ,

∠XYZ =90°

XY =1/2 XZ or XZ=2XY

to prove:

∠YXZ =60 °

Solution:

please refer to the diagram attached below:

Construction:

extend XY to P, so that XY = YP

join P to Z.

Proof:

In ΔXYZ & ΔPYZ,

XY = YP

YZ is common.

∠XYZ = ∠PYZ=90°

So, ΔXYZ ≅ ΔPYZ by SAS congruence.

therefore, XZ = PZ [CPCT]

also XY = 1/2 XZ

OR, XZ=2XY

BUT, XZ=PZ

Hence, XP = XZ = PZ

ΔXPZ is an equilateral triangle. whose all angles measure 60°

so, ∠PXZ =60 °

and, ∠YXZ =60 °

hence, proved.

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