Question

In the given figure , QS Is perpendicular to PR and PQ = QR, Show that Triangle PQS is congruent to Triangle RQS

Answer 1

1) QS is perpendicular to PR and PQ=QR (given)

2) QS=QS (reflexive property)

3) Angles PQS and RQS are right angles (perpendicular lines form right angles)

4) $\angle PQS=\angle RQS$ (all right angles are equal)

5) $\triangle PQS \cong \triangle RQS$ (SAS)