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Transversals & Special Angles. Objectives: 1.) To identify transversals 2.) To identify angles formed by lines and their transversals. Definition. A transversal is a line that intersects two or more coplanar lines in two or more distinct points. Example 1.

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Transversals special angles

Transversals & Special Angles

Objectives:

1.) To identify transversals

2.) To identify angles formed by lines and their transversals

Mrs. McConaughy Geometry


Definition
Definition

A transversalis a line that intersects two or more coplanar lines in two or more distinct points.

Mrs. McConaughy Geometry


Example 1
Example 1

Is linet a transversal? Explain.

t

m

n

t

r

t

s

x y

Mrs. McConaughy Geometry


Example 2
Example 2

Identify each transversal in the figure.

A

B C

AC AB BC

Mrs. McConaughy Geometry


Special angle pairs formed by two lines and a transversal
Special Angle Pairs Formed by Two Lines and a Transversal

Recall, linear pairs of angles and vertical angles!

When a transversal intersects two lines, some special angle pairs are formed.

Mrs. McConaughy Geometry


Special angle pairs formed by two lines and a transversal1
Special Angle Pairs Formed by Two Lines and a Transversal

1 2

34

56

7 8

12

34

5 6

78

Alternate InteriorAngles

Corresponding Angles

1 2

34

56

7 8

12

3 4

5 6

78

Alternate Exterior Angles

Same-Side Interior Angles

Mrs. McConaughy Geometry


Example 3

7 8

5 6

3 4

1 2

Example 3

Identify each given pair of angles as alternate interior, corresponding, alternate exterior, or none of these.

1 & 8

3 & 7

4 & 5

2 & 8

3 & 5

Determine the following:

Corresponding Angles:

< 7 & < 3; < 5 & < 1

< 8 & < 4; < 6 & < 2

Alternate Interior Angles:

< 5 & < 4; < 6 & < 3

Alternate Exterior Angles:

< 7 & < 2; < 8 & < 1

Same-side Interior Angles:

< 5 & < 3; < 6 & < 4

Mrs. McConaughy Geometry


Final checks for understanding
Final Checks for Understanding

1. Define transversal.

2. Given l // m, cut by transversal s, in the figure which follows, name the following:

Corresponding Angles:

Alternate Interior Angles:

Alternate Exterior Angles:

Same-side Interior Angles:

Mrs. McConaughy Geometry


Final checks for understanding1
Final Checks for Understanding

Given l // m, cut by transversal s, name the following:

Corresponding Angles:

Alternate Interior Angles:

Alternate Exterior Angles:

Mrs. McConaughy Geometry


Homework
Homework

Homework: Transversals and Special Angles WS plus text: ________

Mrs. McConaughy Geometry


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