Question

State True or False:

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

Answer 1

Given: ABCD is a rectangle, M, N,S,T is the mid-point of AB,AD,DC,CB respectively
Joint NS,ST,TM,MN, BD and AC.
By Mid point theorem,
$NS\parallel MT\parallel AC$ and $NS=MT=\frac{1}{2}AC$
$MN\parallel ST\parallel BD$ and $MN=ST=\frac{1}{2}BD$
Hence, MNST is a parallelogram. Since, opposite sides are equal and parallel.
Now, $AC=BD$ (Diagonals of rectangle are equal)
Thus, $MN=ST=NS=MT$
Hence, MNST is a rhombus. (Adjacent sides are also equal)

Hence, the statement is False.