2012 · Q66
ABCD is a parallelogram. If the bisectors of the angle A and angle C meet the diagonal BD at points P and Q respectively, then which one of the following is correct?
Elementary MathematicsGeometry
- APCQA is a straight line
- BTriangle APQ is similar to triangle PCQ
- CAP = CP
- DAP = AQ
Explanation
By the angle-bisector theorem BP/PD = AB/AD and BQ/QD = AD/AB, so P and Q are symmetric about the midpoint of BD; the half-turn about it sends triangle APQ onto triangle CQP, making them congruent (hence similar).