Question Number 66981 by Mr Jor last updated on 21/Aug/19
Commented by Mr Jor last updated on 21/Aug/19
$${In}\:{the}\:{figure}\:{above},{ABCD}\:{is}\:{a} \\ $$$${parallelogram}.{AOC}\:{and}\:{BOD}\: \\ $$$${are}\:{diagonals}\:{of}\:{the}\:{parallologram}. \\ $$$${Show}\:{that}\:{the}\:{diagonals}\:{of}\:{the}\: \\ $$$${parallelogram}\:{bisect}\:{each}\:{other}. \\ $$$${Give}\:{reasons}. \\ $$
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](Q67007.png)
$${In}\:\bigtriangleup\:{AOD}\:\:\&\:\bigtriangleup{COB} \\ $$$$\left.\begin{matrix}{\angle{DAO}=\angle{BCO}}\\{\angle{ODA}=\angle{OBC}}\end{matrix}\right\}\left[{reason}\right] \\ $$$${AD}={CB}\:\:\left[{reason}\right] \\ $$$$\Rightarrow\:\bigtriangleup\:{AOD}\:\cong\:\bigtriangleup{COB}\:\:\left[{criteria}\right] \\ $$$$\Rightarrow{AO}={CO}\:\:\&\:{OD}={OB} \\ $$$$\therefore\:{diagonals}\:{of}\:{a}\:\mid\mid^{{gm}} \:{bisect}\:{each}\:{other} \\ $$