Question

State true or false:

The figure obtained by joining the mid-points of the adjacent sides of a rectangle is a Parallelogram.

• A. True
• B. False

Answer 1

The correct option is B False

Given: ABCD is a rectangle, M, N,S,T is the mid-point of AB,AD,DC,CB respectively.
Join NS, ST, TM, MN and the diagonals AC and BD.
In a triangle,the line connecting the mid-points of 2 sides parallel to & equals in length the half of the base
$NS||MT||AC$ and $MN||ST||BD$
$NS=MT=\frac{1}{2}AC$; $MN=ST=\frac{1}{2}BD$
MNST is a parallelogram ...(The opposite sides of a quadrilateral are parallel & equal)
Now, since $AC=BD$ ....(the diagonals of a rectangle equal)
Thus, $MN=NS=ST=TM$ ...(the half of the equal quantities equal)
Hence, MNST is a rhombus ...(All the sides are equal)