By which congruence criterion does the triangle ∆PQR ≅ ∆XYZ, given that ZX = RP, RQ = ZY, and ∠PRQ =∠XZY ?

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Q.

By which congruence criterion does the triangle ∆PQR ≅ ∆XYZ, given that ZX = RP, RQ = ZY, and $∠ P R Q = ∠ X Z Y$ ?

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a

SSS

b

SAS

c

ASA

d

RHS

answer is B.

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Detailed Solution

It is given that in the following triangles, ZX = RP, RQ = ZY, and

∠ P R Q = ∠ X Z Y .

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SAS (side-Angle-side): If under a correspondence, two sides and the angle included between them of one triangle are equal to two corresponding sides and the angle included between them of another triangle, then the triangles are congruent.
We have,
ZX = RP
RQ = ZY

∠ P R Q = ∠ X Z Y

Then by the definition of SAS congruence property,

Δ P Q R ≅ Δ X Y Z

Therefore,

Δ P Q R ≅ Δ X Y Z

by SAS congruence property.
Hence, option (2) is correct.

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By which congruence criterion does the triangle ∆PQR ≅ ∆XYZ, given that ZX = RP, RQ = ZY, and ∠PRQ =∠XZY ?