Prove that the diagonals of a parallelogram bisect each other.

Kristian Combs

Kristian Combs

Answered question

2023-01-23

Prove that the diagonals of a parallelogram bisect each other.

Answer & Explanation

cycloidey29

cycloidey29

Beginner2023-01-24Added 5 answers


Let ABCD be the parallelogram. So AB || DC and AD || BC.
Consider triangle AOD and COB.
AD = BC (opposite sides of a parallelogram)
∠DAO = ∠BCO (Alterante angles)
∠ADO = ∠CBO (Alternate angles)
Therefore, by ASA congruency, the triangle are congruent.
Now AO = OC and BO = OD because they are corresponding sides of two congruent triangle. Thus, the diagonals of a parallelogram bisect each other.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?