Show that the quadrilateral formed by joining the midpoint of the side

1.	Show that the quadrilateral formed by joining the midpoint of the sides is also square
Answer» 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∥

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

Answer»

Answer:

figures

Step-by-step EXPLANATION:

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∥