Question

In ∆AB and ∆PQR AB = QP , LB = LP and BC = PR then these two are congruent by :​

Answer 1

Given:

In ΔABC AND ΔPQR,

AB = QP

∠B = ∠P

BC = PR

To find:

the Congruency of the triangles

Solution

In the ΔABC AND ΔQPR,

AB = QP (SIDE)

∠B = ∠P   (ANGLE)

BC = PR  ( SIDE)

We find from the given data that side AB and QP are equal. The values of angle B and angle P is equal. The value of side BC and side PR is also equal.

This satisfies the SAS criteria of congruence which states that if two sides and the included angle of a triangle are equal to the corresponding sides and included angle of another triangle, then the triangles are congruent.

Using Side-Angle-Side (SAS) Triangle property,

ΔABC AND ΔQPR fullfils the criteria

∴ ΔABC ≅ΔQPR

Answer:  SAS (Side-Angle-Side) Triangle property