6.6 Proportionality Theorems Triangle Proportionality Theorem: A line // to one side of a triangle divides the other sides proportionally. Warning: This proportion is for the pieces of side only--- not the sides. The // segments cannot be found using this proportion! The converse is also true. When a segment divides two sides of a triangle proportionally, the segment is // to the third side of the triangle.

top piece bottom piece = top piece bottom piece

The sides are not proportional, so the segments cannot be parallel. This fraction is the reciprocal.

(TH) If three // lines intersect two transversals, then they divide the transversals proportionally. (TH) If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides. or piece side = piece side AD BD AC BC =

Do on board. This can be done two ways.

Hint: if DF = 14, and DG = x, what are you going to call GF? piece side piece side = x 14-x 8 12 =

Geometry Page 400(1-7,13,16,22,30-36)‏ Page 400(8-12,14,15,17-19,21,23-28)