Question

ABCD is the quadrilateral in which P Q R and S are the mid-points of the sides AB, BC,CD, and DA respectively. Show that PQRS is a Rhombus.​

Answer 1

Answer:

Draw 2 diagonals

then show that Pq = 1/2 of that diagonal

then just like that show it for qr rs ps

then prove that both the diagonals of the quadrilateral are equal

hence Pq=qr=rs=ps

therefore as we know all sides in a rhombus are equal

thus pqrs is a rhombus