Show that the quadrilateral formed by …
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Preeti Dabral 1 year, 10 months ago
Let a square ABCD in which L, M, N & O are the midpoints.
In {tex}\triangle{/tex}AML and {tex}\triangle{/tex}CNO
AM = CO (AB = DC and M and O are the midpoints)
AL = CN (AD = BC and L and N are the midpoints)
{tex}\angle{/tex} MAL = {tex}\angle{/tex}NCO (all angles of a square = 90°)
by AAS criteria
{tex}\triangle{/tex}AML {tex}\cong{/tex} {tex}\triangle{/tex}CNO
{tex}\therefore{/tex} ML = ON (CPCT)
similarly {tex}\triangle{/tex}MBN {tex}\cong{/tex} {tex}\triangle{/tex}LDO
now,
in {tex}\triangle{/tex}AML,
{tex}\angle{/tex}AML = {tex}\angle{/tex}ALM (AM = AL)
= 45°
similarly in {tex}\triangle{/tex}LDO
{tex}\angle{/tex}DLO = 45°
{tex}\therefore{/tex} {tex}\angle{/tex} MLO = 90°
by the properties of SQUARE
All sides are equal and angles are 90°
0Thank You