Question

the diagonal of a parallelogram bisect each other

Answer 1

Answer:

Yes it is true. I want to you to be more precise with you question.

Answer 2

Question :-

The Diagonals diagonals of a parallelogram bisect each other.

Solution:-

Given :- ABCD is a parallelogram with the diagonals AC and BD and the diagonals bisect each other at the point of O.

To Prove:- OB = OD & OA = OC

To Proof:- We know that Opposite sides of parallelogram are parallel

• AD || BC ( With the transveral BD )
• ODA = OBC ---(1) ( Alternate Interior Angles)

Also. AD ||BC ( with the transveral AC)

Same as ODA = OBC --(2)( alternate interior Angles)

Now, In ∆ AOD & ∆ BOC

• OAD = OBC ---( From eqn 1)
• AD = CD ---( Opposite sides)
• ODA = OBC ---( From eqn 2)
• ∆AOD ~ ∆ BOC ---(By ASA Angle side angle Congruency Rule)

By CPCT ( Corresponding parts of congruent Triangles)

=> OA = OC & OB = OD