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rials PORS De respedively on sides AB, Be DA of ABOU such that AP C EC AS . Bove that PORS a parallelogram. Got my

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Q1
Let $$ABCD$$ be a square. Location points $$P, Q, R, S$$ on the sides $$AB, BC, CD, DA$$ respectively such that $$AP=BQ=CR=DS$$. Prove that $$PQRS$$ is a square.
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Q2

Let ABCD be a square. Locate points P, Q, R, S on the sides AB, BC, CD, DA respectively such that AP = BQ = CR = DS. Prove that PQRS is a square.

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Q3
ABCD is a parallelogram, P,Q,R and S are points on sides AB,BC,CD and DA respectively such that AP=DR. If area of parallelogram ABCD is 48 cm2, then find the area of quadrilateral PQRS in cm2.
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Q4
P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and DA of || gm ABCD. Show that PQRS is a parallelogram and also show that
ar|| gm PQRS=12×ar(||gm ABCD).
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Q5
$$P, Q, R, S$$ are respectively the midpoints of the sides $$AB, BC, CD$$ and $$DA$$ of parallelogram $$ABCD$$. Show that $$PQRS$$ is a parallelogram and also show that $$ar (||gm PQRS)=\dfrac{1}{2} \times ar(||gm ABCD)$$.

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