The quadrilateral formed by joining the mid-points of the sides of a quadrilateral taken in order is a:

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Kite

Parallelogram

Rectangle

Square

answer is B.

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Detailed Solution

Given that ABCD is a quadrilateral.
Question Image

Also, P, Q, R, S are the midpoints of AB, BC, CD and AC respectively.
In

Δ A B C

, P is a midpoint of AB and Q is a midpoint of BC, By Midpoint theorem,
PQ =

12 AC

and

P Q | | A C

--------- (1)
In

Δ A D C

, R is a midpoint of CD and S is a midpoint of AD,
By Midpoint theorem,

R S = 12 AC and RS ∥ A C

--------- (2)
From equation (1) and (2) RS∥PQ and RS = PQ
So, PQRS is a parallelogram.
Hence, the correct option is 2.

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