Chapter 3Section 3-1: Properties of

Parallel Lines

Goal 2.02: Apply properties, definitions, and theorems of angles

and lines to solve problems and write problems and write proofs.

Turn in Cumulative Review

Check Skills: p 115 (1-6)

Essential Questions

1. How are angles formed by 2 lines and a transversal identified?

2. How are the properties of parallel lines used to determine angle measure?

Transversal

a line that intersects two or more coplanar lines in different points

Alternate Interior Angles

(alt. int. ‘s) two nonadjacent interior angles on opposite side of the transversal

Same-Side Interior Angles

Also called consecutive angles

(s-s int. ‘s) two interior angles on the same side of the transversal

Corresponding Angles

(corres. ‘s) two angles in corresponding positions relative to the two lines

Examples, p 118

5)

7)

Together: p 118-119 (6,8)

Examples

1) 2 and 3

3) SPQ and PSR

Together: 2, 4

Theorem about Parallel Planes

If two parallel planes are cut by a third plane, then the lines of intersection are parallel.

Example

Use # 9 for 4th property of: if 2 parallel lines are cut by a transversal then ….

P. 119 11.13.15.

P 120Two lines and a transversal form how many pairs

of the following? 19 Alternate interior angles 20 corresponding angles 21 same-side interior angles 22 vertical angles

Postulate and Theorems about angles formed by 2 Parallel lines and a transversal

If two parallel lines are cut by a transversal, then the corresponding angles are congruent. (post)

If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

If two parallel lines are cut by a transversal, then same-side interior angles are supplementary.

If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other also.

Practice

• With a partner: p 119 (12- 16 even) p 120 (23-25 all)Go over.

Individually: Practice 3-1 Worksheet

Summarize

List the 4 things you know if 2 parallel lines are cut by a transversal.

1.2.3.4.

Standardized Test Prep: p. 121 (37-41 all)

Homework

• Mixed Review: p 121 (42- 50 all)• Worksheet: Definitions worksheet Review