Question

in △ jkl and △ pqr, if (overline{jk} cong overline{pq}), (overline{kl} cong overline{qr}), and ( angle k cong angle q ), then ( \triangle jkl ) must be congruent to ( \triangle pqr ).
a. true
b. false

Explanation:

To determine if \(\triangle JKL \cong \triangle PQR\), we use the SAS (Side - Angle - Side) congruence criterion. The SAS criterion states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

We are given that \(\overline{JK}\cong\overline{PQ}\), \(\overline{KL}\cong\overline{QR}\), and \(\angle K\cong\angle Q\). In \(\triangle JKL\), the sides \(\overline{JK}\) and \(\overline{KL}\) form the included angle \(\angle K\). In \(\triangle PQR\), the sides \(\overline{PQ}\) and \(\overline{QR}\) form the included angle \(\angle Q\). Since we have two pairs of congruent sides and the included angle is also congruent, by the SAS congruence postulate, \(\triangle JKL\) and \(\triangle PQR\) must be congruent.

Answer:

A. True