Question

Given: ABCD is a parallelogram and AC bisects BD.
Prove: AB is congruent to BC.

Answer 1

Let's see

In ∆ABE and ∆CBE

• BE=BE(Common side)
• AE=EC[Diagonals of a parallelogram bisect each other]
• <AEB=<BEC[90°]

So by

SAS congruence the triangles are congruent

AB=BC

• Proved

Fact:-

It's already given AC is perpendicular to BD

• It means diagonals are perpendicular to each other

According to general property of rhombus this parallelogram is also a rhombus.

So sides are equal hence AB =BC