In triangle ABC, P is the mid-point of side BC. A line through P and parallel to CA meets AB at ...

AB and CD are the parallel sides of a trapeziuml. E is the mid-point of AD. A line through E and parallel to side AB meets the line BC at point F. Prove that F is the mid-point of BC.

P is the mid-point of side AB of a parallelogram ABCD .A Line through B parallel to PD meets DC at Q and AD produced at R. Prove that ( i )AR=2BC (ii) BR=2BQ.

In the triangle ABC, the base BC is trisected at D and E. The line through D, parallel to AB, meets AC at F and the line through E parallel to AC meets AB at G. Let EG and DF intersect at H. What is the ratio of the sum of the area of parallelogram AGHF and the area of the triangle DHE to the area of the triangle ABC ?

P is the mid-point of side AB of parallelogram ABCD. A line drawn from B parallel to PD meets CD at Q and AD produce at R. Prove that : (i) AR = 2BC (ii) BR= 2BQ

P is a point on the bisector of an angle /_ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.

Draw any triangle ABC. Bisect side AB at D. Through D, draw a line parallel to BC, meeting AC in E. Measure AE and EC .

E is the mid-point of the side AD of the trapezium ABCD with AB||DC . A line through E drawn parallel to AB intersects BC at F. then

In the given figure, in triangle ABC, D is the mid-point cf AB and P is any point on BC. If CQ || PD meets AB in Q and area of triangle ABC = 30 cm2, then, area of triangle BPQ is

P is a point on the bisector of angle ABC .If the line through P,parallel to BA meet at Q ,prove that BPO is an isosceles triangle.