Question

13. If the diagonals of a parallelogram are equal, then show that it is
a
rectangle.

Answer 1

Step-by-step explanation:

Given : Let ABCD be a parallelogram where AC = BD

TO PROVE : ABCD IS A PARALLELOGRAM

PROOF : RECTANGLE is a parallelogram with one angle 90°

we prove that of its interior angle is 90°

In ∆ ABC and ∆ DCB,

AB= DC { OPPOSITE SIDE OF PARALLELOGRAM ARE EQUAL}

BC= BC ( COMMON)

AC= DB( SSS Congruence rule )

AC=DB ( given )

∆ABC=~∆DCB ( SSS CONGRUENCE RULE)

ANGLE ABC = ANGLE DCB ( CPCT )...1

NOW,

AB//DC (OPPOSITE SIDE OF PARALLELOGRAM ARE PARALLEL)

& BC is a transversal

angle B + angle C=180°

2 angle B= 180°

angle B= 180°/2

angle B= 90°

so, ABCD is a parallelogram with one angle 90°

ABCD IS A RECTANGLE.

I hope it will help you

Answer 2

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