Advertisement Remove all ads

Properties of a Parallelogram - Theorem: If in a Quadrilateral, Each Pair of Opposite Angles is Equal, Then It is a Parallelogram.

Advertisement Remove all ads

Topics

theorem

Theorem:  If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.
Proof: In quadrilateral ABCD 
∠A = ∠D  
`=>` ∠A +∠B +∠C + ∠D
Now, ∠A +∠B +∠C + ∠D = 360°  (angle sum property of quadrilateral)
`=>` 2(∠A +∠B ) = 360°  
`=> ` ∠A +∠B  = 180°  
`therefore` ∠A +∠B  = ∠C + ∠D = 180°  
Line AB intersects AD and BC at A and B respectively. 
Such that ∠A +∠B = 180° 
`therefore`  AD || BC   (Sum of consecutive interior angle is 180° ) ...(1)
∠A +∠B  = 180°  
∠A +∠D  = 180°     (∠B= ∠D)
`therefore`  AB || CD  ..(2)
From (1) and (2), we get
AB || CD and AD || BC
`therefore` ABCD is a parallelogram.

If you would like to contribute notes or other learning material, please submit them using the button below.

Shaalaa.com | Theorem : If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram.

Shaalaa.com


Next video


Shaalaa.com


Theorem : If in a quadrilateral, each pair of opposite angles is equal, then it is a parallelogram. [00:13:07]
S
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×