CHAPTER 3 WARM-UPS

WARM-UP #37

Terms and DefinitionsPARALLEL LINES

Coplanar lines that do not intersect

SKEW LINES Noncoplanar lines that are not parallel and do not intersect

PARALLEL PLANES

Planes that do not intersect

QuestionsWhere outside of school may you see parallel lines?

Name a pair of skew lines in this classroom.

Name a pair of parallel planes in this classroom.

WARM-UP #38

Explain, in detail, the four types of angles we learned about last class period. HINT: Use your “Understanding Angles”

handout.

WARM-UP #39

WARM-UP #40

Use your notes and handouts from this chapter to complete the “Theorem” column of the THEOREMS ABOUT PARALLEL LINES table (see the tray). HINT: Write each theorem as a conditional

(if…then) statement.

WARM-UP #41

Khan Academy: Parallel Lines 1

WARM-UP #42

Determine whether each statement is always, sometimes, or never true.

1. Perpendicular lines meet at right angles.

2. Two lines in intersecting planes are perpendicular.

3. Two lines in the same plane are parallel.4. Two lines in parallel planes are

perpendicular.

WARM-UP #43

Solve each equation.

1. 30 + 90 + x = 180

2. 55 + x + 105 = 180

WARM-UP #44

The measure of one angle of a triangle is 115. The other two angles are congruent. What is the measure of each of the congruent angles?

A. 32.5B. 57.5C. 65D. 115

WARM-UP #45

Open your textbook to page 177 and work through problem 31.

HINT: Start by finding the value of either c or e.

WARM-UP #46

Respond to the following questions in your notebook:

1. What are some ways to describe the slope of a line? List as many as you can think of.

2. What is the equation for finding the slope of a line?

WARM-UP #47

Find the slopes of the lines containing the following points:

1. (3,7) and (-4,11)

2. (-4,-4) and (8,14)

WARM-UP #48

Using your knowledge of slope and parallel lines, explain how the slopes of parallel lines are related.

WARM-UP #49

Your classmate tries to find an equation for a line parallel to y = 3x – 5 that contains (-4,2). What is your classmate’s error?

slope of given line = 3 slope of parallel line = 1/3

y – y1 = m(x – x1) y – 2 = 1/3(x + 4)