P, Q, R and S are mid-points of sides AB, BC, CD, and DA, respectively. If the length of a diagonal of the rectangle ABCD is 8 cm, then prove that the quadrilateral PQRS is a rhombus, and find its side length.

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

1.	P, Q, R and S are mid-points of sides AB, BC, CD, and DA, respectively. If the length of a diagonal of the rectangle ABCD is 8 cm, then prove that the quadrilateral PQRS is a rhombus, and find its side length.
Answer» $P, Q, R$ and $S$ are mid-points of sides $A B, B C, C D$ , and $D A$ , respectively. If the length of a diagonal of the rectangle ABCD is $8 c m,$ then prove that the quadrilateral $P Q R S$ is a rhombus, and find its side length.