Easy to hard: Quadrilateral

[ts871]

Doubt- how is the area of all the parts in the rectangle is 1?

In rectangle the diagonal bisect but it does not divide the rectangle into equal parts. So the area can’t be equal. That is the property of square where the diagonal divides into equal parts.

What am i missing ?

[Joan]

@ts871

In rectangle the diagonal bisect but it does not divide the rectangle into equal parts. So the area can’t be equal. That is the property of square where the diagonal divides into equal parts.

The 2 diagonal divides the rectangle into 4 parts each having the same area (not necessarily the same height and base). Regarding the square, the 2 diagonals divide the square into 4 equal triangles all with the same height and base.

[Joan]

The diagonal BF divides the rectangle into 2 equal right-angle triangles.

so, a + b = c + d

The diagonal EA divides the rectangle into 2 equal right-angle triangles.

so, b + c = a + d

You get,

b = d
a = c

In BEF, the line EO cuts the triangle into 2 equal parts,

so a = b = c = d