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# E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

**Solution:**

Given, ABCD is a __parallelogram__

E and F are points on __diagonal__ AC of parallelogram ABCD such that AE = CF

We have to show that BFDE is a parallelogram.

Join the other diagonal BD of the parallelogram.

The diagonal BD meets AC at O

We know that diagonals of a parallelogram bisect each other.

From the figure,

OA = OC

OD = OB

Given, AE = CF

From the figure,

OA - AE = OE

OC - CF = OF

So, OE = OF

Therefore, BDEF is a parallelogram as the diagonals EF and BD bisect each other at O.

**✦ Try This: **In parallelogram ABCD, two point P and Q are taken on diagonal BD such that DP=BQ. Show that △APD ≅ △CQB

**☛ Also Check:** NCERT Solutions for Class 9 Maths Chapter 8

**NCERT Exemplar Class 9 Maths Exercise 8.3 Problem 5**

## E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. Show that BFDE is a parallelogram.

**Summary:**

E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. It is shown that BFDE is a parallelogram since the diagonals EF and BD bisect each other at O

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