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# Parallel Lines and Transversals

The triangle proportionality theorem states if a line parallel to one side of a triangle (or transversal) cuts through the other two sides of the triangle, the line divides these two sides proportionally. In the figure below, the transversal DE is parallel to the triangle side BC and intersects both AB and AC, which means it divides them proportionally.

The triangle proportionality theorem also applies if three or more lines are cut by a transversal. Let''s take a closer look.

## Intersecting three parallel lines with two transversals & example

In the figure below, two transversal lines intersect three parallel lines. These parallel lines separate the transversals into proportional parts:

In other words, if

, then:
AB/BC = DE/EF
,
AC/DF = BC/EF
and
AC/BC = DF/EF.

### Example

Let''s find the value of x:

First, write a proportion.

GJ/HJ = KL/LM

Substitute the values.

8/6 = 10/x

Use the cross-product.

(8)(x) = (10)(6)

8x = 60

Divide each side by 8.

8x/8 = 60/8

x = 7.5

The value of x is 7.5.

## Practice questions on parallel lines and transversals

Answer the following questions using the figure below:

a. If

AB = 5, BC = 6, and DE = 6
, what is the value of
EF
?

First, write a proportion.

AB/BC = DE/EF

Substitute the values.

5/6 = 6/x

Use the cross-product.

(5)(x) = (6)(6)

5x = 36

Divide each side by 5.

5x/5 = 36/5

b. If
BC = 3, DE = 5, EF = 6
what is the value of AB?

Write a proportion.

x/BC = DE/EF

Substitute the values.

x/3 = 5/6

Use the cross-product.

(x)(6) = (5)(3)

6x = 15

Divide each side by 6.

6x/6 = 15/6

Parallel Lines

Midpoint Formula

Platonic Solids

## Flashcards covering the Parallel Lines and Transversals

Common Core: High School - Geometry Flashcards

## Practice tests covering the Parallel Lines and Transversals

Common Core: High School - Geometry Diagnostic Tests