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Question Number 66981 by Mr Jor last updated on 21/Aug/19

Commented by Mr Jor last updated on 21/Aug/19

$I n t h e f i g u r e a b o v e, A B C D i s a$ $p a r a l l e l o g r a m . A O C a n d B O D$ $a r e d i a g o n a l s o f t h e p a r a l l o l o g r a m .$ $S h o w t h a t t h e d i a g o n a l s o f t h e$ $p a r a l l e l o g r a m b i s e c t e a c h o t h e r .$ $G i v e r e a s o n s .$
	Answered by Kunal12588 last updated on 21/Aug/19
	$In △ AOD & △COB {: ((∠DAO=∠BCO)),((∠ODA=∠OBC)) }[reason] AD=CB [reason] ⇒ △ AOD ≅ △COB [criteria] ⇒AO=CO & OD=OB ∴ diagonals of a ∣∣^(gm) bisect each other$
	$I n △ A O D & △ C O B$ $\begin{matrix} ∠ D A O = ∠ B C O \\ ∠ O D A = ∠ O B C \end{matrix}} [r e a s o n]$ $A D = C B [r e a s o n]$ $\Rightarrow △ A O D ≅ △ C O B [c r i t e r i a]$ $\Rightarrow A O = C O & O D = O B$ $∴ d i a g o n a l s o f a ∣ ∣^{g m} b i s e c t e a c h o t h e r$
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