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Question

Which congruence criterion do you use in the following?
Given: RP$$=$$ZX, RQ$$=$$ZY, $$\angle$$PRQ$$=\angle$$XZY. So $$\Delta$$PQR$$\cong\Delta$$XYZ.

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Solution

By SAS congruence criterion,
 since it is given that 
$$RP$$=$$ZX$$, $$RQ$$=$$ZY$$ and $$\angle$$PRQ$$=\angle$$XZY.
 The two sides and one angle in one of the triangle are equal to the corresponding sides and the angle of
 other triangle.
Therefore,
 $$\Delta$$PQR$$\cong\Delta$$XYZ.

Mathematics
NCERT
Standard VII

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