Question

ABCD is an Quadrilateral in which DM and BN are perpendiculars an diagonal AC and DM = BN. Prove that AC bisect BD​

Answer 1

Step-by-step

GivenABCD is a quadrilateral in which diagonals AC and BD intersect each other at P

Also,DN⊥AC and BM⊥AC

DN=BM

In △DNP and △BMP we have

∠DPN=∠BPM since they are vertically opposite angles.

∠DNP=∠BMP since each are equal to 90

∘

DN=BM(given)

⇒△DNP≅△BMP by AAS postulate.

⇒DP=BP=8cms by CPCT

We have BD=BP+DP=8+8=16cms from the diagram.

This means O is mid point of BD.

Hence prove