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Question

Diagonals of a rhombus bisect each other at ______ angles.

A
90°
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B
10°
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C
360°
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D
60°
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Solution

The correct option is A 90°
Let ABCD is a rhombus.
AB=BC=CD=DA [ Adjacent sides are equal in rhombus ]
In ΔAOD and ΔCOD
OA=OC [ Diagonals of rhombus bisect each other ]
OD=OD [ Common side ]
AD=CD
ΔAODΔCOD [ By SSS congruence rule ]
AOD=COD [ CPCT ]
AOD+COD=180° [ Linear pair ]
2AOD=180°
AOD=90°
Hence, the diagonals of a rhombus bisect each other at right angles.

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