Question

show that the quardilateral formed by joining the midpoint of the consecutive sides of square is also a square ​

Answer 1

Step-by-step explanation:

Let ABCD is a square.

AB = BC = CD = AD P,Q,R and S are mid-points of AB,BC,CD and DA, respectively.

Now, in ΔADC, SR||AC and SR = 1/2 AC In ΔABC,

PQ||AC and PQ = 1/2 AC SR||PQ and SR = PQ = 1/2 AC

Similarly, SP||BD and BD||RQ SP||RQ and SP = 1/2 BD And RQ = 1/2 BD SP = RQ = 1/2 BD

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

AC = BD SP = RQ = 1/2 AC SR = PQ = SP = RQ All sides are equal. Now, in quad OERF, OE||FR and OF||ER ∠EOF = ∠ERF = 90

Hence, PQRS is a square