Question

show that the quadrilateral formed by joining the midpoint of the sides is also square​

Answer 1

Answer:

figures

Step-by-step explanation:

solution

In a square ABCD, P,Q,R and S are the mid-points of AB,BC,CD and DA respectively.

⇒  AB=BC=CD=AD           [ Sides of square are equal ]

In △ADC,

SR∥AC and SR=21AC       [ By mid-point theorem ]  ---- ( 1 )

In △ABC,

PQ∥AC and PQ=21AC     [ By mid-point theorem ]  ---- ( 2 )

From equation ( 1 ) and ( 2 ),

SR∥PQ and SR=PQ=21AC    ---- ( 3 )

Similarly, SP∥BD and BD∥RQ

∴  SP∥RQ and SP=21BD

and RQ=21BD

∴  SP=RQ=21BD

Since, diagonals of a square bisect each other at right angle.

∴  AC=BD

⇒  SP=RQ=21AC          ----- ( 4 )

From ( 3 ) and ( 4 )

SR=PQ=SP=RQ

We know that the diagonals of a square bisect each other at right angles.

∠EOF=90o.

Now, RQ∥DB

RE∥FO

Also, SR∥