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Question

In the above figure, it is given that BDEF and FDCE are parallelograms. Can you say that BD=CD? Why or why not?

77981_226545ba8b4d4e3a82c16f0ce3e35220.png

A
Yes
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B
No
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C
May be
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D
Cannot be determined
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Solution

The correct option is A Yes
Given:-
ABC is a triangle. D,EF are points on BC,CA.AB taken in order. BDEF anf FDCE are parallelograms.

To Prove:-
BD=CD

Proof:-
In parallelogram BDEF,
BD=EF(i)[Opposite sides of a parallelogram are equal.]

In parallelogram FDCE,
CD=EF(ii)[Opposite sides of a parallelogram are equal.]

From (i) and (ii),
BD=CD

Hence, proved.

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