Triangle Proportionality Theorem

A transversal is a line that intersects two or several lines.

Theorem: A transversal that is parallel to one of the sides in a triangle divides the other two sides proportionally.

Proof: All you need to know in order to prove the theorem is that the area of a triangle is given by \[A=\frac{w\cdot h}{2}\]

where w is the width and h is the height of the triangle. Compare areas three times!

1. Make a triangle poly1=ΔAED and a triangle poly2=ΔBED. Let poly1 and poly2 denote the areas of the triangles. What is the ratio of poly1 and poly2? Prove your answer!
2. Make a triangle poly3=ΔDEC. What is the ratio of poly3 and poly1? Prove your answer!
3. What is the ratio of poly3 and poly2? Prove your answer!

Show that a/b=c/d!