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Triangles

In quadrilate...

Question

In quadrilateral ABCD, diagonal BD is bisected by the diagonal AC.
then $Δ A B C$ and $Δ A D C$ are equal in area.
State whether the above statement is true or false.

A

True

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B

False

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Solution

The correct option is A True
$I n A B D, C D i s b i s e c t e d b y A B a t P . T h e r e f o r e, A P i s t h e m e d i a n o f A B D . W e k n o w a m e d i a n d i v i d e s t h e a r e a o f a t r i a n g l e i n h a l f . ∴ A r e a (A B P) = A r e a (A D P) - - - (1) I n B C D, B D i s b i s e c t e d b y A C a t P . T h e r e f o r e, A P i s t h e m e d i a n o f A B D . W e k n o w a m e d i a n d i v i d e s t h e a r e a o f a t r i a n g l e i n h a l f . ∴ A r e a (B C P) = A r e a (D C P) - - - (2) A d d i n g e q u a t i o n s 1 & 2, w e g e t A r e a (A B P) + A r e a (B C P) = A r e a (A D P) + A r e a (D C P) \Rightarrow A r e a (A B C) = A r e a (A D C)$

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