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3.1 Parallel Lines and Transversals

- Chapter 3 Angles and Triangles

What is a Transversal?

- Lines in the same plant that do not intersect are

called parallel lines. - Lines that intersect at rights angles are called

perpendicular lines. - Transversal- a line that intersects two or more

lines. - When parallel lines are cut by a transversal,

several pairs of congruent angles are formed.

Corresponding Angles

- When a transversal intersects parallel lines,

corresponding angles are congruent.

Finding Angle Measures

Use the figure to find the measures of (a) lt1 and

(b) lt2.

- (a) lt1 and the 110 degree angles are

corresponding angles. They are congruent - So, the measure of lt1 is 110

- lt1 and lt2 are supplementary, The sum of the

angles is 180 degrees.

Practice

Use the figure to find the measure of lt1 and lt2.

explain your reasoning.

- lt1 and 63 degrees are corresponding angles, sot

lt1 is 63 degrees.

- lt1 and lt2 are supplementary angles.

Using Corresponding Angles

Use the figure to find the measures of the

numbered angles.

- lt1 and the 75 degree angle are vertical angles,

so they are congruent. - So, lt175

- The 75 degree angle is supplementary to both lt2

and lt3. - So, the measures of lt2 and lt3 are 105

Using corresponding angles, the measures of lt4

andlt6 are 75, and the measures of lt5 and lt7 are

105.

Practice

- Use the figure to find the measure of the

numbered angles.

Interior and Exterior Angles

- When two parallel lines are cut by a transversal
- Four interior angles are formed on the inside of

the parallel lines. - Four exterior angles are formed on the outside of

the parallel lines. - lt3, lt4, lt5, and lt6 are interior angles.
- lt1, lt2, lt7, and lt8 are exterior angles.

Using Corresponding Angles

- A store owner uses pieces of tape to paint a

window advertisement. The letters are slanted at

an 80 degree angle. What is the measure of lt1?

- Because all the letters are slanted at an 80

degree angle, the dashed lines are parallel. The

pieces of tape is the transversal. - Using corresponding angles, the 80 degree angle

is congruent to the angle that is supplementary

to lt1.

The measure of lt1 is 180-80100 degrees.

Alternate Interior and Alternate Exterior Angles

- When a transversal intersects parallel lines
- Alternate interior angles are congruent
- Alternate exterior angles are congruent

Identifying Alternate Interior and Alternate

Exterior Angles

The photo shows a portion of an airport. Describe

the relationship between each pair of angles.

- lt3 and lt6 are alternate exterior angles.
- lt3 is congruent to lt6

- lt2 and lt7 are alternate interior angles.
- lt2 is congruent to lt7