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## Answers

: opposite sides eaqual AB=CD and AD=BC

AC=BD |given

AB=BA |common

Therfore triangle ACB is Congurrent to triangle BDA

<ACB = < BAD (1) | by cpct

Again AD || BC

AD || BC and transversal AB intersects thm

<BAD + <ABC =180 (2)| SUm of consecutive interrior angleson the same side of the transversal is 180 degree

FROM (1) and (2)

<BAD=<ABC=90 degree

therfore <A= 90 degree and <b =90 degree

Similarly we can prove <c=90 degree and <D=90 degree

Therfore ABCD is A triangle

NOTE: < is used for ANGLE and ||gm for parallelogram and || for parallel

THANK YOU :)

In ΔADC and ΔBCD

AC=BD(given)

AD=BC(opp. sides of a parallelogram are equal)

CD=CD(common)

∴By SSS congruence rule

ΔADC is congruent to ΔBCD

by cpct

∠ADC=∠BCD

Since in a parallelogram adjacent angles are supplementary

∠ADC+∠BCD=180°

2∠ADC=180°(∠ADC=∠BCD)

∴∠ADC=90°

and since ∠ADC=∠BCD

∠BCD=90°

since in a parallelogram adjacent angles are 90°, the parallelogram is a rectangle.

Hence Proved