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Right Triangle And Midpoints (Posted on 2007-10-31) Difficulty: 3 of 5
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.

See The Solution Submitted by K Sengupta    
Rating: 3.0000 (2 votes)

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Solution a solution | Comment 1 of 3

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
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