Answer with explanation:
A Quadrilateral A B CD, in which diagonals intersect each other at O.
In Δ AOB and ΔCOD
AO=OC-----[Given]
∠AOB=∠COD→→→Vertically Opposite Angles
BO=OD------[Given]
Δ AOB ≅ ΔCOD-------[SAS]
1.⇒AB=CD→→→C PCT
Now, In ΔA OD and Δ B O C
A O=O C-----[Given]
BO=OD-----[Given]
∠AOD=∠BOC→→→Vertically Opposite angles
ΔA OD ≅ Δ B O C------[S AS]
2.⇒ AD=BC→→[C P CT]
From 1 and 2,
If in a Quadrilateral , opposite sides are equal, then it is a Parallelogram.