Question

If Eand F are the two points on AB and CD respectively .Also E is the midpoint of AB
and EF II To AD then F is also a midpoint. a)True b ) False

Answer 1

Answer:

b) False

Step-by-step explanation:

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.

${Sol}^{n} =$

ABCD is ∥gm

AB ∥ CD

AE ∥ FC

⇒ AB = CD

  \frac{1}{2} AB = \frac{1}{2} CD

    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..