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PQRS is a parallelogram
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(i). In triangle ADC , S and R are the mid points of side AD respectively.
In triangle. the line segment joining the mid point of any two side and is half of it .
SR//AC and SR=½AC ________[1]
(ii). In triangle ABC, P and Q are mid points of side AB and BC respectively.
Therefore, by using mid point theorem,
PQ//AC and PQ=½AC ________[2]
(iii). Using equation [1] and [2]
PQ//SR and PQ=SR _______[3]
(iv). From equation [3], we obtain
PQ//SR and PQ=SR
Clearly, one pair of opposite sides of quadrilateral PQRS is parallel and equal.
Hence, PQRS is a parallelogram.
In triangle. the line segment joining the mid point of any two side and is half of it .
SR//AC and SR=½AC ________[1]
(ii). In triangle ABC, P and Q are mid points of side AB and BC respectively.
Therefore, by using mid point theorem,
PQ//AC and PQ=½AC ________[2]
(iii). Using equation [1] and [2]
PQ//SR and PQ=SR _______[3]
(iv). From equation [3], we obtain
PQ//SR and PQ=SR
Clearly, one pair of opposite sides of quadrilateral PQRS is parallel and equal.
Hence, PQRS is a parallelogram.
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