Question

P Q R and S are respectively the midpoints of sides ab, BC, CD and D of quadrilateral ABCD in which AC is equals to BD and ac is perpendicular to bd full stop prove that pqrs is a square

Answer 1

Answer:

Step-by-step explanation:

A quadrilateral whose diagonals are perpendicular to each other can be a square or rhombus only.

So all the sides of it will be equal.And the diagonals are also equal.

Here ABCD is a square, P,Q,R,S are the mid-point of the sides.

As QR || to BD, so form mid-point theorem, QR = 1/2(BD)

Similarly PS= 1/2(BD)

PQ =1/2(AC)

and RS =1/2(AC)

As AC = BD

So PQ = QR = PS =RS

Hence PQRS is a square.