Question

$\huge\red{QUESTION:-}$
If the diagonal of a quadrilateral bisect each other at 90°, then prove that it is a rhombus

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Answer 1

$\bold { \huge\red{A} \green{n} \blue{s} \pink{w} \orange{e} \purple{r} \blue{: - }}$

In Triangle AOB and COD

AO=OC (diagonal bisect)

ANGLE AOB=ANGLE COD(VERTICALLY OPPOSITE)

OB=OD(DIAGONAL BISECT)

BOTH TRIANGLE ARE CONGRUENT BY SAS

AND AB=CD (BY CPCT)

SIMILARLY AD=BC

IN TRIANGLE AOB nd AOD

OB=OD( DIAGONAL)

ANGLE AOD=ANGLE AOB(90°)

AO(COMMON)

BOTH TRIANGLE ARE CONGRUENT BY SAS nd AD=AB BY CPCT

AO AB=BC=CD=AD

(HENCE PROVED)