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A quadrilateral {A}{B}{C}{D} is such that diagonal {B}{D} divi

Question

A quadrilateral $A B C D$ is such that diagonal $B D$ divides its area in two equal parts. Prove that $B D$ bisects $A C ˙$ GIVEN : A quadrilateral $A B C D$ in which diagonal $B D$ bisects it. i.e. $a r (A B D) = a r (B D C)$ CONSTRUCTION : Join $A C$ Suppose $A C$ and $B D$ intersect at $O$ . Draw $A L ⊥ B D$ and $C M B D ˙$ TO PROVE : $A O = O C ˙$

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Elizabeth Discussed

A quadrilateral

A B C D

is such that diagonal

B D

divides its area in two equal parts. Prove that

B D

bisects

A C ˙

GIVEN : A quadrilateral

A B C D

in which diagonal

B D

bisects it. i.e.

a r (A B D) = a r (B D C)

CONSTRUCTION : Join

A C

Suppose

A C

and

B D

intersect at

O

. Draw

A L ⊥ B D

and

C M B D ˙

TO PROVE :

A O = O C ˙

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