Question

In a parallelogram ABCD, two points and Q are taken on its diagonal BD such that DP = BQ. Prove that PQ and AC bisect each other.​

Answer 1

Answer:

Here, ABCD is a parallelogram.

AB∥DC and BD is a transversal.

∴ ∠ABQ=∠CDP [ Alternate angles ] ---- ( 1 )

In △AQB and △CPD,

⇒ AB=CD [ Opposite sides of parallelogram are equal ]

⇒ ∠ABQ=∠CDP [ From ( 1 ) ]

⇒ BQ=DP [ Given ]

∴ △AQB≅△CPD [ By SAS congruence ]

⇒ AQ=CP [ CPCT ]