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Lesson 3-1. Parallel Lines and Transversals. Transparency 3-1. 5-Minute Check on Chapter 2. 1. Make a conjecture about the next item in the sequence: 5, 20, 80, 320. 2. Write the contrapositive for this statement: If you live in Boston, then you live in Massachusetts.

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lesson 3 1

Lesson 3-1

Parallel Lines and Transversals

slide2

Transparency 3-1

5-Minute Check on Chapter 2

1. Make a conjecture about the next item in the sequence: 5, 20, 80, 320.

2. Write the contrapositive for this statement:

If you live in Boston, then you live in Massachusetts.

3. Use the Law of Detachment or the Law of Syllogism to determine whether a valid conclusion can be reached from the following set of statements: If two angles form a linear pair and are congruent, they are both right angles. A and B are both right angles.

4. Name the property that justifies the statement.

If m1 + m2 = 75 and m2 = m3, then m1 + m3 = 75.

5. Find m1 and m2 if m1 = 8x + 18, and m2 = 16x – 6.

6. The measures of two complementary angles are in the ratio 7:8. What is the measure of the larger angle?

Standardized Test Practice:

96

A

42

B

C

84

D

48

slide3

Transparency 3-1

5-Minute Check on Chapter 2

1. Make a conjecture about the next item in the sequence: 5, 20, 80, 320.

1280

2. Write the contrapositive for this statement:

If you live in Boston, then you live in Massachusetts.

If you do not live in Massachusetts, then you do not live in Boston.

3. Use the Law of Detachment or the Law of Syllogism to determine whether a valid conclusion can be reached from the following set of statements: If two angles form a linear pair and are congruent, they are both right angles. A and B are both right angles.

no conclusion

4. Name the property that justifies the statement.

If m1 + m2 = 75 and m2 = m3, then m1 + m3 = 75.

Substitution Property

5. Find m1 and m2 if m1 = 8x + 18, and m2 = 16x – 6.

m1 = 74; m2 = 106

6. The measures of two complementary angles are in the ratio 7:8. What is the measure of the larger angle?

Standardized Test Practice:

96

A

42

B

C

84

D

48

objectives
Objectives
  • Identify the relationships between two lines or two planes
  • Name angles formed by a pair of lines and a transversal
vocabulary
Vocabulary
  • Parallel symbol (||)
  • Parallel lines – coplanar lines that do not intersect
  • Parallel planes – planes that do not intersect
  • Skew lines – lines that do not intersect and are not coplanar
  • Transversal – a line that intersects two or more coplanar lines at different points
solving angle problems

t

k

1

2

3

4

5

6

l

7

8

Solving Angle Problems
  • 95% of all angle problems are solved by one of two equations:
    • Angle = Angle (angles are congruent)
    • Angle + Angle = 180 (angles are supplementary)

Angle = Angle

m1 = m4

3x + 10 = 4x – 30

+30 = +30

3x + 40 = 4x

-3x = -3x

40 = x

Angle + Angle = 180

m1 + m2 = 180

4x – 30 + x + 10 = 180

5x – 20 = 180

+20 = +20

5x = 200

x = 40

slide8

Name all segments that intersect

Answer:

Given the following figure:

Name all planes that are parallel to plane AEF.

Answer: plane BHG

slide9

Name all segments that are parallel to

Name all segments that are skew to

Answer:

Answer:

Given the following figure:

slide10

a. Name all planes that are parallel to plane RST.

b.

Answer:

c.

Answer:

d.

Answer:

Use the figure to name each of the following.

Answer: plane XYZ

slide11

BUS STATION Some of a bus station’s driveways are shown as lines u, v, w, x, y and z.

Identify the sets of lines to which line vis a transversal.

Answer: If the lines are extended, line v intersects lines u, w, x, and z.

Identify the sets of lines to which line yis a transversal.

Answer: lines u, w, x, z

slide12

BUS STATION Some of a bus station’s driveways are shown as lines u, v, w, x, y and z.

Identify the sets of lines to which line uis a transversal.

Answer: lines v, x, y, z

Identify the sets of lines to which line wis a transversal.

Answer: lines v, x, y, z

slide13

a. line a

b. line b

c. line c

d. line d

HIKING A group of nature trails is shown. Identify the sets of lines to which each given line is a transversal.

Answer: lines c, d, e, f

Answer: lines c, d, e, f

Answer: lines a, b, d, e, f

Answer: lines a, b, c, e, f

slide14

Given the following figure, identify each set of angles as alternate interior, alternate exterior, corresponding, or consecutive interiorangles.

Answer: corresponding

Answer: alternate exterior

Answer: consecutive interior

Answer: alternate interior

slide15

d.

a.

b.

e.

c.

f.

Identify each set of angles as alternate interior, alternate exterior, corresponding, or consecutive interiorangles.

Answer: consecutive interior

Answer: corresponding

Answer: alternate exterior

Answer: alternate interior

Answer: corresponding

Answer: alternate exterior

summary homework
Summary & Homework
  • Summary:
    • Coplanar lines that do not intersect are called parallel
    • When two lines are cut by a transversal, there are many angle relationships
  • Homework:
    • pg 129 – 131: 11-17, 70-75