# Prove that the quadrilateral formed by joining the midpoints of consecutive sides of a square is also a square. Please it's urgent

1
by kusumsharmaskm

## Answers

2015-02-08T10:28:54+05:30

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

in triangle AML and triangle 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
triangle AML CONGRUENT to triangle CNO
therefore ML = ON  ( CPCT  )
similarly in triangle MBN CONGRUENT to  LDO  and
AND triangle  AML is CONGRUENT  to triangle
now ,
in Triangle AML ,
angle AML = angle ALM ( AM = AL )
= 45 degree
similarly in triangle LDO
angle DLO = 45 degree
there fore ,
angle MLO = 90 degree

by the properties of SQUARE
all sides are equal and angles are 90 degree