Parallelogram

It is a quadrilateral where

both pairs of opposite sides are parallel

i.e. AB ∥ DC and AD ∥ BC

Properties of Parallelogram:

1. Opposite sides are equal
   AB = CD & AD = BC
   
   
2. Opposite angles are equal
   ∠A = ∠C and ∠B = ∠D
   
   

3. Adjacent angles are supplementary

     ∠A + ∠B = 180°

     ∠A + ∠D = 180° 

     ∠C + ∠D = 180°    

     ∠B + ∠C = 180°
   

4. Diagonals bisect each other

   AO = CO and BO = DO

Proof : Class 9 th − Chapter 8 Theorem 8.6

     5.Diagonals divides the Parallelogram into two congruent triangles

       ∆ ABC ≅ ∆ CDA and 

       ∆ BAD ≅ ∆ DCB

Proof : Class 9 th − Chapter 8 Theorem 8.1