PQR is a right angled triangle with hypotenuse PQ while PR = √2 and QR = 1. S is the midpoint of PQ and T is the midpoint of PR. The line segments QT and RS intersect at the point U.

Determine Angle QUR.

Let P,Q, and R have coordinates (0,sqrt(2)), (1,0), and (0,0) respectively. So S and T have coordinates (.5,sqrt(2)/2) and (0,sqrt(2)/2), respectively. -->

The slopes of segments RS and TQ are sqrt(2) and -sqrt(2)/2

--> Product of slopes is -1, so angle QUR is a right angle.

Posted by Dennis on 2007-10-31 09:13:01