## ABCD-is-a-parallelogram-P-and-Q-are-two-points-on-the-diagonal-BD-such-that-DP-QB-Prove-that-APCQ-is-a-parallelogram?

Question

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## Answers ( )

A quadrilateral in which both pairs of opposite sides are parallel is called a

ParallelogramStep-by-step explanation:A quadrilateral is said to be parallelogram if

From the question given above

ABCD is a parallelogram and P and Q are points on BD such thatDP=QBIn ΔAPD and ΔCQB,————————–(i)

DP = QB (Given)

∠ADP = ∠CBQ

(Alternate interior angles)AD = BC

(Hence it is proved that -Opposite sides of a parallelogram are equal)so, ΔAPD ≅ ΔCQB (As per SAS congruence rule)

If , ΔAPD ≅ ΔCQB.————————-(ii)

AP = CQ ( by CPCT )

In ΔAQB and ΔCPD,———————–(iii)

BQ = DP (Given)

∠ABQ = ∠CDP (

Alternate interior angles)AB = CD (

Opposite sides of a parallelogram)so, ΔAQB ≅ ΔCPD (

As per SAS congruence rule)(iv) AQ = CP (

According to CPCT as ΔAQB ≅ ΔCPD.)From (ii) and (iv) equation ,we can say that

AP=CQ ,

AQ=CP

It is proved that APCQ has equal opposite sides also it has equal opposite angles.Hence,APCQ is a Parallelogram