ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig) . AC is a diagonal. Show that: (i) SR || AC and SR = 1/2 AC (ii) PQ = SR (iii) PQRS is a parallelogram.


P, Q, R and S are the mid points of quadrilateral ABCD


 Theorem :The line segment joining the mid-points of two sides of a triangle is parallel to the third side.

(i)  SR || AC and SR = 1/2 AC

Considering ∆ACD

we observe that S and R are the mid points of side AD and DC respectively. [Given]

Hence,SR || AC and SR = ½ AC (As per the above theorem)…………………….(1)

(ii) PQ = SR

Considering ∆ACB

We observe that P and Q are the mid points of side AB and BC respectively. [Given]

Hence, PQ || AC and PQ = ½ AC (As per above theorem)…………………………(2)

From (1) and (2) we can say,


(iii) PQRS is a parallelogram

rom (i) and (ii) we can say that

PQ || AC and SR || AC

so, PQ || SR and PQ = SR 

If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

Hence, PQRS is a parallelogram.

Was this answer helpful?


0 (0)

Upvote (0)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *




Free Class