1800-212-7858 (Toll Free)
9:00am - 8:00pm IST all days
8104911739

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

022-62211530

Mon to Sat - 11 AM to 8 PM

# In a parallelogram ABCD, E and F are mid points of sides AB and CD. Show that line segment AF and CE trisect the diagonal BD.

Asked by Topperlearning User 4th June 2014, 1:23 PM

ABCD is a parallelogram.

AB || CD

And hence, AE || FC

Again, AB = CD (Opposite sides of parallelogram ABCD)

AB =CD

AE = FC (E and F are mid-points of side AB and CD)

In quadrilateral AECF, one pair of opposite sides (AE and CF) is parallel and equal to each other.

Therefore, AECF is a parallelogram.

In DCQ,

DF = CF (given)

PF||QC

DP = PQ ....(i) (by converse of mid-point them)

In ABP,

AE = BE (given)

AP || EQ

PQ = QB ….(ii) (by converse of mid-point them)So, DP = PQ = QB

Hence, line segment AF and CE trisect the diagonal BD.

Answered by Expert 4th June 2014, 3:23 PM
• 1
• 2
• 3
• 4
• 5
• 6
• 7
• 8
• 9
• 10

You have rated this answer /10