1. Course 3, Lesson 5-1
1. Describe a situation that could be
represented by the graph.
2. The graph shows the relationship between
a person’s annual income and age.
Write a statement about what happens
to the income as age increases.
2. Course 3, Lesson 5-1
ANSWERS
1. Sample answer: A van frequently stops to pick up
passengers.
2. The income is increasing.
3. HOW can algebraic concepts be
applied to geometry?
Geometry
Course 3, Lesson 5-1
5. To
• classify the angles formed when two
lines are cut by a transversal,
• find missing angle measures when two
parallel lines are cut by a transversal
Course 3, Lesson 5-1
Geometry
7. Course 3, Lesson 5-1
Geometry
A line that intersects two or more lines is called a
, and eight angles are formed.transversal
Interior angles
Exterior angles
Alternate interior angles
Alternate exterior angles
Corresponding angles
lie inside the lines.
Examples: 3, 4, 5, 6
lie outside the lines
Examples: 1, 2, 7, 8
are interior angles that lie on opposite sides of the
transversal. When the lines are parallel, their measures are equal.
Examples: 4 6; m 3 5m m m
are exterior angles that lie on opposite sides of
the transversal. When the lines are parallel, their measures are equal.
Examples: 1 7; 2 8m m m m
are those angles that are in the same position on the two
lines in relation to the transversal. When the lines are parallel, their measures are
equal. Examples: 1 5; 2 6; 4 8; 3 7m m m m m m m m
8. 1
Need Another Example?
Step-by-Step Example
1. Classify the pair of angles in the figure
as alternate interior, alternate exterior,
or corresponding.
∠1 and ∠7
∠1 and ∠7 are exterior angles that lie on
opposite sides of the transversal. They
are alternate exterior angles.
10. 1
Need Another Example?
Step-by-Step Example
2. Classify the pair of angles in the figure
as alternate interior, alternate exterior,
or corresponding.
∠2 and ∠6
∠2 and ∠6 are in the same position on the two
lines. They are corresponding angles.
12. 1
Need Another Example?
Step-by-Step Example
3. A furniture designer built the bookcase
shown. Line a is parallel to line b.
If m∠2 = 105°, find m∠6 and m∠3.
Justify your answer.
Since ∠2 and ∠6 are supplementary,
the sum of their measures is 180°.
m∠6 = 180° – 105° or 75°
2 Since ∠6 and ∠3 are interior angles
that lie on opposite sides of the
transversal, they are alternate interior
angles. The measures of alternate
interior angles are equal. m∠3 = 75°
13. Answer
Need Another Example?
Mr. Adams installed the gate
shown. Line c is parallel to line
d. If m∠4 = 40°, find m∠6 and
m∠7. Justify your answer.
m∠6 = 40° and m∠7 = 140°; Sample answer:
∠4 and ∠6 are alternate interior angles, so they
are congruent. ∠6 and ∠7 are supplementary.
Since m∠6 = 40°, m∠7 = 140°.
14. 1
Need Another Example?
2
3
4
Step-by-Step Example
4. In the figure, line m is parallel to
line n, and line q is perpendicular
to line p. The measure of ∠1 is
40°. What is the measure of ∠7?
Since ∠1 and ∠6 are alternate
exterior angles, m∠6 = 40°.
40 + 90 + m∠7 = 180
Since ∠6, ∠7, and ∠8 form a straight line,
the sum of their measures is 180°.
So, m∠7 is 50°.
15. Answer
Need Another Example?
In the figure, line a is parallel to line b,
and line c is perpendicular to line d.
The measure of ∠7 is 125°. What is
the measure of ∠4?
35°
16. How did what you learned
today help you answer the
HOW can algebraic concepts be applied
to geometry?
Course 3, Lesson 5-1
Geometry
17. How did what you learned
today help you answer the
HOW can algebraic concepts be applied
to geometry?
Course 3, Lesson 5-1
Geometry
Sample answers:
• When two parallel lines are cut by a transversal,
analyze the figure to determine missing measures.
• Write and solve an equation to find the missing
measures.
18. Describe the pairs of
congruent angles in a set of
parallel lines cut by a
transversal.
Course 3, Lesson 5-1
Ratios and Proportional RelationshipsFunctionsGeometry
