Does diagonal of a rectangle divides the rectangle into two equal areas
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the point where the diagonals intersect divided each diagonals into two equal parts. each diagonals divided rectangle into two congruent right triangles.....
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yes diagonal divide a rectangle into two equal parts
let a rectangle ABCD
such that AB=CD
AD=BC
and diagonal AC
then triangles are
ACD and BAC
area of triangle ACD is
1/2×AD×CD---------eq. 1
area of triangle BAC is
1/2×AB×BC---------eq. 2
as AB=CD
AD=BC
then putting values in equation 1
1/2×BC×AB=area of triangle BAC
so by this it is proved that both triangles are equal and diagonal divide the rectangle into two equal parts
let a rectangle ABCD
such that AB=CD
AD=BC
and diagonal AC
then triangles are
ACD and BAC
area of triangle ACD is
1/2×AD×CD---------eq. 1
area of triangle BAC is
1/2×AB×BC---------eq. 2
as AB=CD
AD=BC
then putting values in equation 1
1/2×BC×AB=area of triangle BAC
so by this it is proved that both triangles are equal and diagonal divide the rectangle into two equal parts
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