Question

E and F are mid-points of sides AB and CD respectively of a parallelogram ABCD. AF
and CE intersect diagonal BD in P and Q respectively. Prove that diagonal BD is trisected at P and Q​

Answer 1

Step-by-step explanation:

proof:-IN triangle APB

proof:-IN triangle APB E is the mid point of AB or AQ parallel AP

proof:-IN triangle APB E is the mid point of AB or AQ parallel APso Q is the mid point of PB.

proof:-IN triangle APB E is the mid point of AB or AQ parallel APso Q is the mid point of PB. PQ=QB. (EQUATION 1)

proof:-IN triangle APB E is the mid point of AB or AQ parallel APso Q is the mid point of PB. PQ=QB. (EQUATION 1)Similarly, p is the mid point of QD

proof:-IN triangle APB E is the mid point of AB or AQ parallel APso Q is the mid point of PB. PQ=QB. (EQUATION 1)Similarly, p is the mid point of QD QP=DP (EQUATION 2)

proof:-IN triangle APB E is the mid point of AB or AQ parallel APso Q is the mid point of PB. PQ=QB. (EQUATION 1)Similarly, p is the mid point of QD QP=DP (EQUATION 2)from 1 and 2 we get PQ=QB=DP

proof:-IN triangle APB E is the mid point of AB or AQ parallel APso Q is the mid point of PB. PQ=QB. (EQUATION 1)Similarly, p is the mid point of QD QP=DP (EQUATION 2)from 1 and 2 we get PQ=QB=DP HENCE PROVED