Question

If the diagonals of a rhombus are equal, prove that it is a square.
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Answer 1

Answer:

ABCD is a rhombus, in which diagonals AC and BD are equal.

We know that diagonals of rhombus bisect each other.

As AC=BD

∴AO=BO=CO=DO

In △AOB,

⇒AO=OB and ∠AOD=90°

∴∠OAB=∠OBA=

2

90

o

=45°

Similarly in △AOD,

⇒∠OAD=∠ODA=45°

∴∠A=∠OAB+∠OAD=45

o

+45

o

=90°

Similarly,

⇒∠B=∠C=∠D=90°

here, AB=BC=CD=DA

∴ Quadrilateral ABCD is a square.