# CBSE Class 9 Answered

**ABCD is a parallelogram. E and F are the mid points of the sides AB and CD respectively. Prove that the segments CE and AF trisect the diagonal BD.**

Asked by Topperlearning User | 16 Aug, 2017, 03:10: PM

Expert Answer

AE||CF and AE = CF (halves of opposite sides of a parallelogram)

Therefore, AECF is a parallelogram.

So, EC||AF

In DPC, FQ||CP and F is the mid point of DC

So, PQ = QD

(Line through the mid point of one side of triangle and parallel to the another side, bisects the third side)

Similarly in ABQ, BP = PQ

Hence, BP = PQ = QD

Thus, CE and AF trisect the diagonal BD.

Answered by | 16 Aug, 2017, 05:10: PM

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