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.

Answer 1

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.