Question

ABCD is a quadrilateral in which all the four angles are equal. Show that AB | CD
and AD Il BC​

Answer 1

Question:

ABCD is a quadrilateral in which all the four angles are equal. Show that AB || CD and

AD Il BC.

Given:

•ABCD is a quadrilateral

•In quadrilateral all the sides are equal.

Solution:

ABCD is a quadrilateral having all angles equal.

Let the angle be x

∴ x + x + x + x = 360°

=4x = 360°

= x = 360/4

= x = 90°

Since,

∠O + ∠A

= 90°+90° =180°(sum of interior angles)

∴ AB || CD

And,

∠A + ∠B

=90°+90° =180°(sum of interior angles)

Therefore, AD || BC. Proved✔️

Answer 2

Solution

Given,

• ABCD is a quadrilateral
• all the for angles of the quadrilateral are equal .

To Prove ,

• AD parallel to BC

So,

as we know that ABCD is a quadrilateral having all angles equal .

• Let the angles be "x" .

Now ,

• it will form a equation like this : x+x+x+x= 360°

now solving this we get ;

$= > x + x + x + x = 360$

$= > 4x = 360$

$= > x = \frac{360}{4}$

$\bold{ = > x = 90 \degree}$

Hence , it all angles are 90 degree.

As ,

angle O + angle A

= 90° + 90°

= 180° [ angle sum property ]

So,

• AB || CD

And ,

angle A + Angle B

= 90° +90°

= 180° [ angle sum property ]

So, it is proved AD || BC