Chapter 3 section 1
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Chapter 3 Section 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.

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Chapter 3 Section 1

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Chapter 3 section 1

Chapter 3Section 1

Parallel Lines and Transversals


Warm up

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 up1

Warm-Up

L

M

N

Q

P

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

No because they are not on the same line.


Warm up2

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 up3

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

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

3

4


Vocabulary cont

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

5

6

l

7

8

1

2

m

3

4


Chapter 3 section 1

  • 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


Chapter 3 section 1

  • 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

H


Chapter 3 section 1

  • 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

l

1

2

3

4

6

5

8

7

10

9

m

11

12

t


Chapter 3 section 1

  • 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

l

1

8

10

2

5

t

11

4

12

6

7

3

9


Chapter 3 section 1

  • 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

1

9

6

11

2

8

4

5

t

3

7

10

12


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