Question

In the parallelogram ABCD, dots divide AB and CD in two equal parts and AD and BC in three equal parts

Answer 1

In a parallelogram ABCD,E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.

ABCD is ∥gm

AB∥CD

AE∥FC

⇒AB=CD

    21AB=21CD

    AE=EC

AECF is ∥gm

In △DQC

F is mid point of DC 

FP∥CQ

By converse of mid point theorem P is mid point of DQ

⇒DP=PQ     (1)

∴AF and EC bisect BD

In △APB

E is mid point of AB

EQ∥AP

By converse of MPT ( mid point theorem )

Q is mid point of PB

⇒PQ=QB   (2)

By (1) and (2)

⇒PQ=QB=DP

AF and EC bisect BD..