Question

the adjoining figure shows a parallelogram abcd in which p is the midpoint of ab and q is the midpoint of cd prove that ae=ef=fc​

Answer 1

Step-by-step explanation:

ANSWER

Since E and F are mid-points AB and CD respectively.

∴AE=BE=

2

1

AB and CF=DF=

2

1

CD

But, AB=CD

∴

2

1

AB=

2

1

CD⇒BE=CF

Also, BE∥CF [∵AB∥CD]

∴ BEFC is a parallelogram.

⇒BC∥EF and BE=PH ...(i)

Now, BC∥EF

⇒AD∥EF [∵BC∥AD as ABCD is a ∥

gm

]

⇒AEFD is a parallelogram

⇒AE=GP ...(ii)

But, E is the mid-point of AB.

∴AE=BE

⇒GP=PH [Using (i) and (ii)]

solution

Answered By

toppr

95 Views

How satisfied are you with the answer?

This will help us to improve better

answr

Get Instant Solutions, 24x7

No Signup required

girl

More Questions by difficulty

EASY

MEDIUM

HARD

Prev Question

Next Question