Question

Prove that the figure obtained by joining the mid points of the adjacent sides of rectangle is a rhombus.

Answer 1

Given: ABCD is a rectangle, M, N,S,T is the mid-point of AB,AD,DC,CB respectively.
To prove: MNST is a rhombus.
Proof: (1) Joint NS,ST,TM,MN (constructions)
............(2) NS=MT=0.5AC; MN=ST=0.5BD (In a triangle,the line connecting
..................the mid-points of 2 sides // to & equals in length the half of the base)
............(3) MNST is a //-gram ( The opposite sides of a quadrilateral are // & equal)
............(4) AC=BD (the diagonals of a rectangle equal)
............(5) MN=NS=ST=TM (the half of the equal quantities equal)
............(6) MNST is a rhombus ( 4 sides are equal)