Question

The figure formed by joining the midpoints of the adjacent sides of a square is a

(a) rhombus

(b) square

(c) rectangle

(d) parallelogram

Answer 1

Let a square ABCD in which L, M, N&O are the midpoints.

In $△$ AML and $△$ CNO

AM = CN ( AB = DC and M and O are the midpoints )

AL = CM ( AD = BC and L and N are the midpoints )

$\angle$ MAL = $\angle$ NCO ( all angles of a square = 90 degree )

by AAS critaria, $△$ AML $\cong$ to $△$ CNO

therefore ML = ON ( CPCT )

similarly in $△$ MBN $\cong$ LDO and
now ,
in $△$ AML ,
$\angle$ AML = $\angle$ ALM ( AM = AL ) = 45 degree
similarly in $△$ LDO
$\angle$ DLO = 45 degree
there fore ,
$\angle$ MLO = 90 degree

By the properties of the square,
all sides are equal and angles are 90 degree