Question

Q.prove that a line segment joining mid point of the adjacent sides of a quadrilateral form a parallelogram​

Answer 1

Step-by-step explanation:

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Answer 2

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Let ABCD be a given Quadrilateral in which P,Q,R and S are the midpoints of AB,BC,CD and DA respectively

In △ABC the points P and Q are the midpoints of sides AB and BC respectively

$∴PQ∥AC$

And

$PQ = \frac{1}{2} AC$

(BY MID-POINT THEOREM) ----------(1)

Once again :

In△DAC the points S and R are mid points of side

AD and CD respectively

$∴SR||AC$

(Also by mid point theorem) ----------(2)

and

$SR = \frac{1}{2} AC$

From eq (1) and (2) we get

$PQ||SR \: \: and \: \: PQ=SR$

Hence Quadrilateral PQRS is a parallelogram