Chapter 3-5

- Proving Lines Parallel

Lesson 3-5 Ideas/Vocabulary

- Recognize angle conditions that occur with

parallel lines.

- Prove that two lines are parallel based on given

angle relationships.

Standard 7.0 Students prove and use theorems

involving the properties of parallel lines cut by

a transversal, the properties of quadrilaterals,

and the properties of circles. (Key) Standard

16.0 Students perform basic constructions with a

straightedge and compass, such as angle

bisectors, perpendicular bisectors, and the line

parallel to a given line through a point off the

line. (Key)

Transitive property of Parallels

- If two lines are parallel to the same line, then

they are parallel to each other. - If p // q and q // r, then p // r.

Reminders from Section 1

- We will use these same theorems to prove the

lines are parallel given certain angle

information.

Corresponding Angle Theorem

- If two parallel lines are cut by a transversal,

then corresponding angles are congruent. - // lines ? corresponding ?s are ?

Corresponding Angle Theorem

Alternate Interior Angle Theorem

- If two parallel lines are cut by a transversal,

then alternate interior angles are congruent. - // lines ? Alt. Int. ?s are ?

Alternate Interior Angle Theorem

Alternate Exterior Angle Theorem

- If two parallel lines are cut by a transversal,

then alternate exterior angles are congruent. - // lines ? Alt. Ext. ?s are ?

Alternate Exterior Angle Theorem

Consecutive Interior Angle Theorem

- If two parallel lines are cut by a transversal,

then consecutive interior angles are

supplementary. - // lines ? Consec. Int. ?s are Supp.

Consecutive Interior Angle Theorem

1

2

m?1 m?2 180

Two ? Theorem

- If two lines are perpendicular to the same line,

then they are parallel to each other. - If m ? p and n ? p, then m // n.

Lesson 3-5 Postulates

Animation Construct a Parallel Line Through a

Point not on Line

Lesson 3-5 Theorems

Lesson 3-5 Example 1

Identify Parallel Lines

- Determine which lines, if any, are parallel.

Consec. Int. ?s are supp.

77o

? a//b

Alt. Int. ?s are not ?

? a is not // c

Consec. Int. ?s are not supp.

? b is not // c

Lesson 3-5 CYP 1

Determine which lines, if any are parallel.I. e

fII. e gIII. f g

- A
- B
- C
- D

I only II only III only I, II, and III

Lesson 3-5 Example 2

Solve Problems with Parallel Lines

Lesson 3-5 Example 2

If Alt. Ext. angles are ?, then the lines will

be //

11x 25 7x 35 Substitution 4x 25

35 Subtract 7x from each side. 4x 60 Add 25 to

each side. x 15 Divide each side by 4.

Lesson 3-5 Example 2

Solve Problems with Parallel Lines

7(15) 35 x 15 140 Simplify.

Lesson 3-5 CYP 2

- A
- B
- C
- D

Lesson 3-5 Example 3

Prove Lines Parallel

Lesson 3-5 Example 3

Prove Lines Parallel

Lesson 3-5 CYP 3

Given x y and , can you use

theCorresponding Angles Postulate to prove a

b?

- A
- B
- C

yes no not enough informationto determine

Lesson 3-5 Example 4

Slope and Parallel Lines

- Determine whether p q.

slope of p

slope of q

Answer Since the slopes are equal, p q.

Lesson 3-5 CYP 4

Determine whether r s.

- A
- B
- C

Yes, r is parallel to s. No, r is not parallel to

s. It cannot be determined.

Homework

- Chapter 3-5
- Pg 175
- 1 5, 7 19, 23 (proof), 24(proof), 37, 50 52