Parallelograms Theorem 1

Ask a Question, Get an Answer!

Type your question here

Hundreds of tutors are online and ready to help you right now!

Statement

The diagonals of a parallelogram bisect each other.

Given:

ABCD is a parallelogram in which diagonals AC and BD

intersect each other at O.

To prove:

The diagonals AC and BD bisect each other i.e, AO=OC and BO=DO.

Proof:

AB||CD (by definition of parallelogram)

AC is a transversal.

(alternate angles are equal in a parallelogram)

Also AB=DC (opposite sides are equal in a parallelogram)

Now in D AOB and D COD,

AB=DC (opposite sides of parallelogram are equal)

(proved by (i))

D AOBD COD (AAS congruency condition)

AO=OC and OB=OD (corresponding parts of congruent triangles are congruent)

i.e., the diagonals of a parallelogram bisect each other.

We have proved one of the properties of a parallelogram by logical deductions.