What if you were given the street map, below, of Washington DC and told to find the missing street lengths?

### Parallel Transverals

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.

#### Solving for an Unknown Value

1. Find

The three lines are marked parallel, so you can set up a proportion.

2. Find

To solve, set up a proportion.

#### Solving for an Unknown Value that Makes Lines Paralell

Find the value of

To solve, set up a proportion and solve for

#### Earlier Problem Revisited

To find

From this,

To find

### Example

#### Example 1

Find

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.

There are several ratios you can use to solve this example. To solve for

### Review

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 andB ? - What is the distance between points
C andD ? - What is the distance between points
A andD ?

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-thirdd , thena is ____________________. - If
c is two timesa , thenb is ____________________. This is a map of lake front properties. Find a andb , the length of the edge of Lot 1 and Lot 2 that is adjacent to the lake.

### Review (Answers)

To view the Review answers, open this PDF file and look for section 7.9.