Question

ABCD is a parallelogram. P and Q are two points on the diagonal BD such that DP=QB.Prove that APCQ is a parallelogram. ​

Answer 1

Answer:

AQ=CP

Step-by-step explanation:

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 ]

Answer 2

Question-

In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP =BQ (see fig). show that APCQ is a parallelogram.

Answer-

We have a parallelogram ABCD, BD is the diagonal and points P and Q are such that PD = QB

In a quadrilateral APCQ,

Opposite sides are equal. [Proved]

∴ APCQ is a parallelogram.