Question

if a parallelogram is cyclic, then it is a rectangle? justify​

Answer 1

As we know the sum of opposite angle is supplementary [90°] .

And in a parallogram opposite angles are equal.

Let them be ‘x’

→ x+x =180°

→ x = 90°

Hence all angles are 90°

♦Therefore it is a rectangle as opposite side are equal and opposite angles are equal also.

♦Hence it is a rectangle______!!!!

Hope it helps (°_°)(+_+)

THANKS

Answer 2

Answer:

The ABCD is a cyclic parallelogram

Then ∠A=∠C (Opposite angle of parallelogram )

In cyclic parallelogram ABCD

∠A+∠C=180

0

(Sum of Opposite angle of cyclic parallelogram=180 degree )

⇒2∠A=180

0

⇒∠A=

2

180

=90

0

And ∠B=∠D (Opposite angle of parallelogram )

In cyclic parallelogram ABCD

∠B+∠D=180

0

(Sum of Opposite angle of cyclic parallelogram=180 degree )

⇒2∠B=180

0

⇒∠B=

2

180

=90

0

So in parallelogram ABCD all angle are right angle then ABCD is a rectangle