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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