Question

if the diagonals of a parallelogram are equal then show that is a recetangle

Answer 1

Answer:

parllelogram and rectangle are quadrtrells. they have 4 sides.

when the sides of rectangle are commpresed it becum parallelogram

Answer 2

Heya mate, Here is ur answer

Refer to the attachment for figure

Given: AC=BD

ABCD is a parallelogram.

To prove : ABCD is a rectangle.

Proof: In ∆ ABD and ∆ABC

AB=AB ( common side)

BD= AC (given)

AD=BC (opposite sides of parallelogram are equal)

So, ∆ ABD congruent ∆ABC (SSS congruence criterion)

So, angle ADB = angle ABC (by CPCT) -----(1)

But

angle ADB + angle ABC =180° (co-interior angles, adjacent angles of parallelogram)

angle ADB +angle ABC =180° (from equation 1)

2 angle ADB =180°

angle ADB=180°/2

Angle ADB=90°

Since, ABCD is a parallelogram with an angle =90° , we can say it as a rectangle.

Hence proved.

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@Laughterqueen

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