CK-12 Foundation: Chapter7ParallelLinesandTransversalsA
Brightstorm: Proportional Segments Between Parallel Lines
The Triangle Proportionality Theorem states 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.
The three lines are marked parallel, so you can set up a proportion.
To solve, set up a proportion.
Watch this video for help with the Examples above.
CK-12 Foundation: Chapter7ParallelLinesandTransversalsB
Concept Problem Revisited
Pairs of numbers are proportional if they are in the same ratio. Two lines are parallel if they have the same slope and thus never intersect. A transversal is a line intersecting a system of lines.
Look at the corresponding segments. Only the segment marked “2” is opposite a number, all the other segments are opposite variables. That means we will be using this ratio, 2:3 in all of our proportions.
Find the value of each variable in the pictures below.
The street map shows part of New Orleans. Burgundy St., Dauphine St. and Royal St. are parallel to each other. If Spain St. is perpendicular to all three, find the indicated distances.
- What is the distance between points A and B?
- What is the distance between points C and D?
- What is the distance between points A and D?
Using the diagram, answer the questions.
- What is the value of w?
- What is the value of x?
- What is the value of y?
- What is the length of AB¯¯¯¯¯¯¯¯?
- What is the length of AC¯¯¯¯¯¯¯¯?
Using the diagram, fill in the blank.
- If b is one-third d, then a is ____________________.
- If c is two times a, then b is ____________________.
This is a map of lake front properties. Find a and b, the length of the edge of Lot 1 and Lot 2 that is adjacent to the lake.