Lesson 3-1

Parallel Lines and Transversals

5-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 2 Transparency 3-1

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 m1 + m2 = 75 and m2 = m3, then m1 + m3 = 75.

5. Find m1 and m2 if m1 = 8x + 18, and m2 = 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:

A CB D42 48 84 96

5-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 25-Minute Check on Chapter 2 Transparency 3-1

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 m1 + m2 = 75 and m2 = m3, then m1 + m3 = 75.Substitution Property

5. Find m1 and m2 if m1 = 8x + 18, and m2 = 16x – 6.m1 = 74; m2 = 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:

A CB D42 48 84 96

Objectives

• Identify the relationships between two lines or two planes

• Name angles formed by a pair of lines and a transversal

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

Angles formed by Transversals

Name Definition ExamplesExterior angles Angles outside the two lines 1, 2, 7, and 8

Interior angles Angles in-between the two lines 3 , 4, 5, and 6

Consecutive Interior angles

In-between lines on the same side of the transversal

3 and 5, 4 and 6

Alternate exterior angles

Outside the two lines on opposite sides of the transversal

1 and 8, 2 and 7

Alternate interior angles

In-between the two lines on opposite sides of the transversal

3 and 6, 4 and 5

Corresponding angles

Occupy similar positions in relation to transversal and lines

1 and 5, 2 and 6, 3 and 7, 4 and 8

tk

l

1 23 4

5 67 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

m1 = m4 3x + 10 = 4x – 30 +30 = +303x + 40 = 4x-3x = -3x 40 = x

Angle + Angle = 180

m1 + m2 = 180 4x – 30 + x + 10 = 180 5x – 20 = 180 +20 = +20 5x = 200 x = 40

tk

l

1 23 4

5 67 8

Name all planes that are parallel to plane AEF.

Answer: plane BHG

Name all segments that intersect

Answer:

Given the following figure:

Name all segments that are parallel to

Answer:

Given the following figure:

Name all segments that are skew to

Answer:

Use the figure to name each of the following.

Answer: plane XYZ a. Name all planes that are parallel to plane RST.

b.

c.

d.

Answer:

Answer:

Answer:

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

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

Identify the sets of lines to which line v is a transversal.

Identify the sets of lines to which line y is a transversal.

Answer: lines u, w, x, z

Identify the sets of lines to which line u is a transversal.

Answer: lines v, x, y, z

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 w is a transversal.

Answer: lines v, x, y, z

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

a. line a

b. line b

c. line c

d. line dAnswer: lines a, b, c, e, f

Answer: corresponding

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

Answer: alternate exterior

Answer: consecutive interior

Answer: alternate interior

Answer: consecutive interior

Answer: corresponding

Answer: alternate exterior

a.

b.

c.

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

Answer: alternate interior

Answer: corresponding

Answer: alternate exterior

d.

e.

f.

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