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Chapter 3 Section 1

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Chapter 3Section 1

Parallel Lines and Transversals

Warm-Up

L

M

N

Q

P

1) Are points L, M, and Q collinear?

2) Find the measure of MN if LM = 5x – 4, MN = 6x + 1, and LN = 30?

3) Name an acute angle, an obtuse angle, and a right angle in the figure.

4) Are <LMP and <NMQ complementary?

Warm-Up

L

M

N

Q

P

2) Find the measure of MN if LM = 5x – 4, MN = 6x + 1, and LN = 30?

Use the segment addition postulate.

LN = LM + MN

30 = 5x – 4 + 6x + 1

30 = 11x – 3

33 = 11x

3 = x

Plug 3 in for x in the equation for MN.

MN = 6x + 1

MN = 6(3) + 1

MN = 18 + 1

MN = 19

Warm-Up

L

M

N

Q

P

3) Name an acute angle, an obtuse angle, and a right angle in the figure.

Acute angle - <LPM or <QMN

Obtuse angle- <PMN or <LMQ

Right angle- <PMQ

4) Are <LMP and <NMQ complementary?

Yes because they form a straight line with <PMQ. So

<LMP + <NMQ + <PMQ = 180

<LMP + <NMQ + 90= 180

<LMP + <NMQ = 90 (Definition of complementary)

Vocabulary

Parallel lines: Two lines that never meet. (Lines l and m are parallel)

Skew lines: Two lines are skew if they do not intersect and are not in the same plane.

Transversal: A line that intersects two or more lines in a plane at different points. (Line t is the transversal)

Exterior Angles- In the figure, transversal t intersects lines l and m. The exterior angles are <3, <4, <5, and <6.

Interior Angles- In the figure, transversal t intersects lines l and m. The interior angles are <1, <2, <7, and <8.

t

5

6

l

7

8

1

2

m

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4

Vocabulary Cont.

Consecutive Interior Angles- In the figure, transversal t intersects lines l and m. <7 and <1, and <8 and <2 are consecutive interior angles.

Alternate Interior Angles- In the figure, transversal t intersects lines l and m. <7 and <2, and <8 and <1 are alternate interior angles.

Alternate Exterior Angles- In the figure, transversal t intersects lines l and m. <5 and <4, and <6 and <3 are alternate exterior angles.

Corresponding Angles- In the figure, transversal t intersects lines l and m. <5 and <1, <7 and <3, <6 and <2, and <8 and <4 are corresponding angles.

t

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l

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- Example 1: Refer to the figure at the right.
- a) Name all planes parallel to the plane ADH.
- Plane BCG
- b) Name all the segments that intersect AT.
- Line segments AB, AC, and AD
- c) Name all the segments that are parallel to AT.
- Line segments DH, BK, and CG
- d) Name all segments that are skew to CG.
- Line segments TK, TH, AD, and AB

B

C

A

D

G

K

T

H

- Example 2: Refer to the figure at the right.
- a) Name all planes that are parallel to plane ABC.
- Plane TKG
- b) Name all segments that intersect AB.
- Line segments BC, AC, AD, AT, and BK
- c) Name all the segments that are parallel to KG.
- Line segments BC, AD, and TH
- d) Name all segments that are skew to TK.
- Line segments CG, DH, AD, AC, and BC

B

C

A

D

G

K

T

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- Example 3: Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
- a) <1 and <8
- Alternate Exterior Angles
- b) <7 and <10
- Alternate Interior Angles
- c) <8 and <12
- Corresponding Angles
- d) <1 and <5
- Corresponding Angels
- e) <4 and <6
- Consecutive Interior Angles
- f) <8 and <9
- Alternate Interior Angles

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t

- Example 4: Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles.
- a) <6 and <10
- Consecutive Interior Angles
- b) <9 and <11
- Alternate Interior Angles
- c) <1 and <5
- Corresponding Angles
- d) <3 and <8
- Alternate Exterior Angels
- e) <7 and <12
- Alternate Interior Angles
- f) <4 and <8
- Corresponding Angles

m

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t

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- Example 5: Refer to the figure showing three lines and the angles formed by these lines.
- A) Identify the transversal to lines l and m.
- Line t
- B)Identify the special name given to each pair of angles
- <7 and <12
- Corresponding Angles
- <8 and <10
- Alternate Interior Angles
- <2 and <12
- Alternate Exterior Angles

l

m

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