In a triangle XYZ, XY = YZ, then which of the following is true?

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∠X=∠Y

∠Y=∠Z

∠Z=∠X

∠X=∠Y=∠Z

answer is C.

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Detailed Solution

A triangle is a three-sided polygon with three angles subtended between the three sides.
When any two sides of a triangle are the same , it is called an isosceles triangle.
Here it is given that XY = YZ, the two sides are equal, hence the triangle XYZ is an isosceles triangle.
For an isosceles triangle, the angles opposite to the equal sides are equal.
Question Image

Let us prove the statement. Construct a median YP from the vertex Y of the triangle.
Consider the triangles XYP and ZYP, P is the midpoint of XZ, and hence, we have:
XY=YZ
XP=ZP
YP=YP
Hence, the triangles XYP and ZYP are congruent to each other by SSS (Side-Side-Side) criterion.
ΔXYP≅ΔZYP
The corresponding angles of congruent triangles are equal, then, we have:
∠Z=∠X
So ,option C)∠Z=∠X is the correct answer.

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