Question

Prove that ABCD is a parallelogram​

Answer 1

Step-by-step explanation:

GIVEN: E is mid point of DC

ABCD IS A PARALLELOGRAM

AE bisects angle A

BE bisects angle B

In triangle ABE

Angle EBA= Angle EBC ...........[i]

(BE bisects angle B)

Angle EBA =Angle BEC .........[ii]

(V.OA)

In triangle BEC

Angle EBC =Angle BEC (from [i] and [ii] )

therefore,BC =EC

(sides opposite to equal angles are equal)

BC =1/2 CD (SINCE E is the mid point)

2BC =CD

AB =2BC

(AB=CD , Opposite side of parallelogram are equal)

Hence proved