Question

if the diagonals of a parallelogram are equal then show I
that it is a triangle ​

Answer 1

Answer:

Given.Let ABCD be a parallelogram

where AC=BD

To prove.ABCD is a rectangle

Proof.rectangle is a parallelogram with one angle 90°

we prove that one of its interior angles in 90°

In ∆ABC=∆DCB

AB= DC. (opposite sides of a parallelogram are equal)

BC=BC. (Common)

AC=DB. (Given)

therefore ∆ABC =~ ∆DCB (SSS congruence rule )

=angleABC =angleDCB (CPCT)

AB || DC (opposite sides of parallelogram are parallel)

&BC is a transversal

therefore angleB + angleC = 180°

(interior angle on the same side of transversal are supplementry )

angleB+ angleB = 180° ( from 1: angleB = angleC )

2angleB = 180°

angleB=180°/2=90°

So,ABCD is a parallelogram with one angle 90°

therefore ABCD is a rectangle

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