SOLUTION: Line segment PQ and PR are congruent sides of isosceles triangle PQR. The bisector of angel P meets line segment QR at K. Prove PK is perpindicular to QR.

Question 377942: Line segment PQ and PR are congruent sides of isosceles triangle PQR. The bisector of angel P meets line segment QR at K. Prove PK is perpindicular to QR.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
First we must show that triangles PKQ and PKR are congruent. PK is in both triangles, PQ = PR, and angle QPK = angle KPR (as PK is an angle bisector). Therefore, by SAS, the two triangles are congruent. This means that angle PKQ = angle PKR = 90 degrees (as the two angles are supplementary) so PK is perpendicular to QR.
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