Same chapter1 markDifficulty: Medium
A quadrilateral whose diagonals bisect each other at right angles is a:
Rectilinear Figures
3 marksDifficulty: Medium
Prove that the diagonals of a parallelogram bisect each other.
Original Khojo Papers practice question — not from a past board paper.
Answer
Let the diagonals AC and BD of parallelogram ABCD meet at O. In triangles AOB and COD, AB = CD as opposite sides, angle OAB = angle OCD and angle OBA = angle ODC as alternate angles. So the triangles are congruent by ASA, and hence AO = OC and BO = OD.
No citable source has been recorded for this record. Treat it as practice material, not as fact.
Explanation
The converse also holds and is often used to prove that a quadrilateral is a parallelogram.
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