By which congruence criterion does the triangle ∆ABC ≅ ∆XYZ?

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SSS

SAS

ASA

RHS

answer is B.

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Detailed Solution

The given triangles are,
Question Image

SAS (side-Angle-side): If under a correspondence, two sides and the angle included between them of a triangle are equal to two corresponding sides and the angle included between them of another triangle, then the triangles are congruent.
From ∆ABC and ∆XYZ,
BC = YZ {from figure}
AC = ZX {from figure}

∠ A C B = ∠ Y Z X {from figure}

Then by the definition of SAS congruence property,
∆ABC ≅ ∆XYZ
Therefore, ∆AMP ≅ ∆AMQ by SAS congruence property.
Hence, option (2) is correct.

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