Question

In a parallelogram ABCD,p and q are the points on line DB such that PD=BQ show that APCQ is a parallelogram.

Answer 1

Answer with Step-by-step explanation:

PD=BQ

By definition of parallelogram

AB=CD

AD=BC

$AB\parallel CD,AD\parallel BC$

$AD=BC$

Reason: By definition of parallelogram

$PD=BQ$

Reason: Given

$\angle PDA=\angle QBC$

Reason: Alternate interior angle theorem

$\triangle$APD$\cong\triangle$BQC

Reason:SAS postulate

$AP=CQ$

Reason: CPCT

$AB=CD$

Reason:By definition of parallelogram

BQ=AP

Reason: Given

$\angle ABQ=\angle CDP$

Reason: Alternate interior angle theorem

$\triangle$ABQ$\cong\triangle$DCP

Reason: SAS postulate

AQ=PC

Reason: CPCT

When opposite sides of quadrilateral area equal then, the quadrilateral is a parallelogram.

Therefore, APCQ is a parallelogram.

Hence, proved.

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Answer 2

Answer:

PD=BQ

By definition of parallelogram

AB=CD

AD=BC

AB || CD, AD || BC AB ∥CD , AD∥BC

AD=BC AD=BC

Reason: By definition of parallelogram

PD=BQ PD=BQ

Reason: Given

∠ PDA= ∠ QBC ∠PDA=∠QBC

Reason: Alternate interior angle theorem

△ APD ≅△ BQC

Reason:SAS postulate

AP=CQ AP=CQ

Reason: CPCT

AB=CD AB=CD

Reason:By definition of parallelogram

BQ=AP

Reason: Given

∠ABQ=∠CDP

Reason: Alternate interior angle theorem

△ ABQ≅△ DCP

Reason: SAS postulate

AQ=PC

Reason: CPCT

When opposite sides of quadrilateral area equal then, the quadrilateral is a parallelogram.

Therefore, APCQ is a parallelogram.

Hence, proved.

Step-by-step explanation:

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