Parallel Lines and Proportional Parts

Warm Up Solve each proportion. 1. 2. 3. 4.

Triangle Proportionality: If a line is parallel to one side of a triangle and intersects the other two, then it separates the sides into segments of proportional lengths.

Find US. Find PN.

A segment whose endpoints are the midpoints of 2 sides of a triangle is parallel to the third side and its length is ½ the length of the third side.

If three or more parallel lines intersect 2 transversals, then they cut off the transversals proportionally.

Suppose that an artist decided to make a larger sketch of the trees Suppose that an artist decided to make a larger sketch of the trees. In the figure, if AB = 4.5 in., BC = 2.6 in., CD = 4.1 in., and KL = 4.9 in., find LM and MN to the nearest tenth of an inch.

What is wrong with these proportions?

EC // AB. Find x and y.

Find x and y.

Find x so that BD // AE. ED = 8, DC = 20, BC = 25, AB = x. BC = 12, AB = 6, ED = 8, DC = X – 4. ED = X – 5, DC = 15, CB = 18, AB = X – 4.

Find PS and SR.

Find AC and DC.

Lesson Quiz Find the length of each segment. 1. 2.