Four
triangles with the same area
In the original figure, because the way the additional triangles were
constructed by using squares on the sides of the orange triangle, we
have that angles α and β are supplementary, and AB is
congruent to BE.
The purple triangle is rotated 90˚ around B, and D is the image of E
Convince yourself of the following and give a reason why
a) AB and BD form a straight line.
b) AB is congruent to BD
c) The orange triangle and the purple triangle have
the same height
d) The orange triangle and the purple triangle have
the same area
e) The same arguments can be given for the yellow
and the blue triangle
Older students can relate c) to the fact that the sine of supplementary
angles is the same.
