Question

Match the following pairs of triangles with their corresponding congruency criteria.

• A. SAS criterion
• B. ASA criterion
• C. SSS criterion

Answer 1

In the above case, we first note that $\angle PQR={60}^{\circ }$ (Angle sum property).

Now, AB = PQ, BC = QR and
$\angle PQR=\angle ABC={60}^{\circ }.$

Thus, the triangles are congruent by SAS criterion.


In this case, $\angle ABC=\angle PQR,$
BC = QR and $\angle ACB=\angle PRQ$.
Thus, the triangles are congruent by ASA criterion.


In this case, we note that $\angle ACB=\angle PQR={60}^{\circ }$
(Angle Sum Property).

We also note that when all angles of a triangle are ${60}^{\circ },$ then the triangle is equilateral.
Thus, we have AB = BC = AC = PQ = QR = PR = 6 cm and by SSS criterion, the triangles are congruent.