CHAPTER 3SECTION 1

Parallel Lines and Transversals

WARM-UP

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?

L M N

Q

P

WARM-UP

1) Are points L, M, and Q collinear? No because they are not on the same line.

L M N

Q

P

WARM-UP

2) Find the measure of MN if LM = 5x – 4, MN = 6x + 1, and LN = 30?Use the segment addition postulate.LN = LM + MN30 = 5x – 4 + 6x + 130 = 11x – 333 = 11x3 = x

L M N

Q

P

Plug 3 in for x in the equation for MN.MN = 6x + 1MN = 6(3) + 1MN = 18 + 1MN = 19

WARM-UP

3) Name an acute angle, an obtuse angle, and a right angle in the figure.Acute angle - <LPM or <QMNObtuse angle- <PMN or <LMQRight 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)

L M N

Q

P

VOCABULARYParallel 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

4321 m

l87

65

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

4321 m

l87

65

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

A

H

G

D

CB

T

K

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

A

H

G

D

CB

T

K

Example 3: Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. a) <1 and <8Alternate Exterior Angles

b) <7 and <10Alternate Interior Angles 

c) <8 and <12Corresponding Angles 

d) <1 and <5 Corresponding Angels 

e) <4 and <6Consecutive Interior Angles 

f) <8 and <9Alternate Interior Angles

l

1211

109

87

65

4321

t

m

Example 4: Identify each pair of angles as alternate interior, alternate exterior, corresponding, or consecutive interior angles. a) <6 and <10Consecutive Interior Angles 

b) <9 and <11Alternate Interior Angles 

c) <1 and <5Corresponding Angles 

d) <3 and <8 Alternate Exterior Angels 

e) <7 and <12Alternate Interior Angles 

f) <4 and <8Corresponding Angles

l

1211

10

9

8

76

54

3

2

1

t

m

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 <10Alternate Interior Angles 

<2 and <12Alternate Exterior Angles

l m

1

t3

2

74

9

810

11

12

6

5