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Q.

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


Question Image

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a

SSS

b

SAS

c

ASA

d

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}
∠ACB=∠YZX                {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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