Here we will discuss about a quadrilateral is a parallelogram if its diagonals bisect each other.
Given: PQRS is a quadrilateral whose diagonals PR and QS bisect each other at O, i.e., OP = OR and OQ = OS.
To prove: PQRS is a parallelogram.
Proof: In ∆OPQ and ∆ORS,
OP = OR, OQ = OS (Given);
∠POQ = ∠ROS (Opposite angles).
Therefore, ∆OPQ ≅ ∆ORS (by SAS criterion of congruency)
Therefore, ∠OPQ = ∠ORS (CPCTC).
So, PQ ∥ SR (From equal alternate angles).
Similarly, from ∆OQR and ∆OSP we get PS ∥ QR.
Therefore, PQRS is a parallelogram.
From A Quadrilateral is a Parallelogram if its Diagonals Bisect each Other to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Oct 04, 24 09:47 AM
Oct 04, 24 01:28 AM
Oct 03, 24 03:22 PM
Oct 03, 24 02:22 PM
Oct 03, 24 01:13 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.