In a `triangleABC` P and Q are points on AB and AC respectively and PQ||BC. Prove that the median AD bisects PQ.

In a Delta ABC , let P and Q be points on AB and AC respectively such that PQ || BC . Prove that the median AD bisects PQ.

In a triangle A B C , let P and Q be points on AB and AC respectively such that P Q || B C . Prove that the median A D bisects P Q .

AD is a median of triangleABC . A straight line parallel to BC intersect AB and AC at P and Q respectively. Prove that AD bisects PQ.

In triangleABC, /_C= 90^(@) and P and Q are the midpoints of BC and AC respectively. Prove that AP^(2)+ BQ^(2)= 5PQ^(2) .

ABCD is a square. P, Q and Rare the points on AB, BC and CD respectively, such that AP = BQ = CR. Prove that: PQ = QR

D is any point on the side BC of DeltaABC . P and Q are centroids of DeltaABD and DeltaADC respectively. Prove that PQ||BC .

O is a point within the ∆ABC . P, Q , R are three points on OA , OB and OC respectively such that PQ||AB and QR||BC . Prove that RP||CA .