http://www.ck12.org Chapter 7. Similarity
7.9 Parallel Lines and Transversals
Here you’ll learn how to use the Triangle Proportionality Theorem with multiple parallel lines.
What if you were given the street map, below, of Washington DC and told to find the missing street lengths?RStreet,
QStreet, andOStreet are parallel and 7thStreet is perpendicular to all three.RandQare one “city block” (usually
1
4 mile or 1320 feet) apart. The other given measurements are on the map. What arexandy? After completing this
Concept, you’ll be able to solve problems like this one.
Watch This
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter7ParallelLinesandTransversalsA
MEDIA
Click image to the left for more content.Brightstorm:Proportional Segments Between Parallel Lines
Guidance
TheTriangle Proportionality Theoremstates that if a line parallel to one side of a triangle intersects the other two
sides, then it divides those sides proportionally. We can extend this theorem to a situation outside of triangles where
we have multiple parallel lines cut by transverals.
Theorem:If three or more parallel lines are cut by two transversals, then they divide the transversals proportionally.
Example A
Finda.
The three lines are marked parallel, so you can set up a proportion.
a
20=
9
15
180 = 15 a
a= 12