the sides PQ and RQ of a parallelogram PQRS are produced to L and M such that PQ =QL and - Maths - Areas of Parallelograms and Triangles

Question

the sides PQ and RQ of a parallelogram PQRS are produced to L
and M such that PQ =QL and RQ= QM to form another paralleogram QLNM
prove that area of pallgm PQRS=area of parllgm QLNM

Ankush Jain · Accepted Answer

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Given are two parallelograms PQRS and QLNM
having PQ = QL and RQ = QM
To prove: Ar(parallelogram PQRS) =
Ar(parallelogram QLNM)
Proof:
Given, PQRS is a parallelogram
â‡’ PQ = RS and PS = QR (1) [Opposite sides of
a parallelogram are parallel and equal to each other]
Now, PQ = QL and PS = RQ implies that
QL = RS and QM = PS (2)
Again, QLNM is also a parallelogram
â‡’ QL = MN and QM = LN (3) [Again, opposite
sides of a parallelogram are parallel and equal to each other]
From (1), (2) and (3), we get
PQ = RS = QL = MN
and PS = QR = QM = LN
As two sets of opposite sides of both the parallelogram are
equal
So, both the parallelograms are congruent to each other
Hence, Ar(parallelogram PQRS) = Ar(parallelogram QLNM) [Hence
proved]

the sides PQ and RQ of a parallelogram PQRS are produced to L and M such that PQ =QL and RQ= QM to form another paralleogram QLNM prove that area of pallgm.PQRS=area of parllgm QLNM