[tex] \pink{ \underline{ \large{ \frak{Q uestion : }}}}[/tex]
Prove that each diagonal of a rhombus bisect each other at 90°
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[tex] \pink{ \underline{ \large{ \frak{Q uestion : }}}}[/tex]
Prove that each diagonal of a rhombus bisect each other at 90°
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To Prove :
Solution :
➥ Let the rhombus be ABCD.
⟹ AB = DA [ Adjacent sides are equal ]
In △AOD and △COD
⟹ OA=OC [ diagonals bisects at each other ]
⟹ OD=OD [ common point ]
⟹ AD=CD
➥ Therefore : △AOD =△COD
⟹ ∠AOD = ∠COD
⟹ ∠AOD + ∠COD = 180°
⟹ 2∠AOD = 180°
⟹ ∠AOD = 180÷2
↬ Hence, proved that the diagonals of a rhombus bisect each other at right angle.