stuck on how to go about with this problem
so I guess I need to show PQR or PQS is 90 deg.
any ideas?
yes, i have an idea. the problem is a lot easier than you think. all you need to know is that angles in a triangle sum to 180 degrees. (oh yeah, and you need to know about similar triangles as well, corresponding sides and angles are proportional. indeed, if hey share a corresponding side, then all corresponding sides and angles are exactly equal)
In triangles PQR and PSQ,
$\displaystyle \angle PRQ = \angle PSQ $(data)
RQ = QS (Q is the midpoint of RS)
PQ is common
Hence, triangles PQR and PSQ are congruent (SAS)
$\displaystyle \angle PQR = \angle PQS $(corresponding angles in congruent triangles are equal)
180 degrees = $\displaystyle \angle PQR + \angle PQS $(angle sum of straight $\displaystyle \angle RQS $equals 180 degrees)
Therefore, $\displaystyle \angle PQR = \angle PQS $= 90 degrees
Hence, PQ is perpendicular to RS.