Question

5. Prove that the quadrilateral formed by joining the midpoints of a quadrilateral is
a parallelogram.

Answer 1

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Correct Question:-

• Prove that the quadrilateral formed by joining the midpoints of a quadrilateral forms parallelogram.?

$\sf\star \: \underbrace\red{Required\:Answer} \: \star$

(i) In ΔDAC,

• R is the mid point of DC and S is the mid point of DA.

Thus by mid point theorem,

• SR || AC and SR = 1/2 AC

(ii) In ΔBAC,

• P is the mid point of AB and Q is the mid point of BC.

• Thus by mid point theorem, PQ || AC and PQ = 1/2 AC

also, SR = 1/2 AC

also, SR = 1/2 ACThus, PQ = SR

(iii) SR || AC

• from (i) and, PQ || AC - from (ii)
• SR || PQ - from (i) and (ii)

also, PQ = SR

Thus, PQRS is a parallelogram.

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Answer 2

(i) In ΔDAC,

R is the mid point of DC and S is the mid point of DA.

Thus by mid point theorem,

SR || AC and SR = 1/2 AC

(ii) In ΔBAC,

P is the mid point of AB and Q is the mid point of BC.

Thus by mid point theorem, PQ || AC and PQ = 1/2 AC

also, SR = 1/2 AC

also, SR = 1/2 ACThus, PQ = SR

(iii) SR || AC

from (i) and, PQ || AC - from (ii)

SR || PQ - from (i) and (ii)

also, PQ = SR

Thus, PQRS is a parallelogram.