UNIT 5 • SIMILARITY, RIGHT TRIANGLE TRIGONOMETRY, AND PROOF
Lesson 6: Proving Theorems About Triangles
Instruction
Guided Practice Skill 5
Example 1
In trigonometry class, Mason used a motion detector to create a graph of his position over time. He
started at a point 2.4 feet in front of the motion detector. Then, he walked away from the motion
detector in a straight line, with a speed of 3.8 feet per second for 6 seconds. Graph the line that
represents his position from 0 seconds to 6 seconds, and then determine the slope of this line using
the slope formula.
1. I dentify the two quantities in the problem that vary and create a
table to show the relationship between them.
The two quantities described that vary are Mason’s position and the
amount of time he walked.
Mason’s position can be determined by multiplying the time by 3.8
(his speed), and then adding 2.4 to include his starting point of 2.4 feet.
Choose several values for the time, from 0 to 6 seconds, and calculate
Mason’s position.
3.8(0) + 2.4 = 2.4
3.8(1) + 2.4 = 6.2
3.8(3) + 2.4 = 13.8
3.8(4) + 2.4 = 17.6
3.8(6) + 2.4 = 25.2
Use a table to organize the information.
Time (seconds)
0
1
3
4
6
Position (feet)
2.4
6.2
13.8
17.6
25.2
U5-242
CCSS IP Support Supplement for Math II
5.6 Skill 5 Prerequisite Skills
© Walch Education
UNIT 5 • SIMILARITY, RIGHT TRIANGLE TRIGONOMETRY, AND PROOF
Lesson 6: Proving Theorems About Triangles
Instruction
2. Graph the relationship.
Use the table of values to graph the relationship, then connect the points.
Because Mason’s position depends on time, time is the independent
variable (x) and position is the dependent variable (y).
Let x represent the amount of time Mason has been walking and let y
represent his position.
30
y
28
26
24
22
Position (feet)
20
18
16
14
12
10
8
6
4
2
0
x
1
2
3
4
5
6
7
8
9
10
Time (seconds)
U5-243
© Walch Education
CCSS IP Support Supplement for Math II
5.6 Skill 5 Prerequisite Skills
UNIT 5 • SIMILARITY, RIGHT TRIANGLE TRIGONOMETRY, AND PROOF
Lesson 6: Proving Theorems About Triangles
Instruction
3. Determine the slope and what it means in the context of the problem.
y2 − y1
Determine the slope by using the slope formula, slope =
. Any
x2 − x1
two points on the graph can be chosen to substitute into the slope
formula. For example, let (x1, y1) be (0, 2.4) and let (x2, y2) be (6, 25.2).
Substitute these values into the slope formula, and then simplify.
slope =
slope =
slope =
y2 − y1
x2 − x1
(25.2) − (2.4)
(6) − (0)
22.8
6
slope = 3.8
Slope formula
Substitute 25.2 for y2, 2.4 for
y1, 6 for x2, and 0 for x1.
Subtract.
Simplify.
The slope is 3.8, or 3.8 feet per second. This verifies the given
information in the problem that Mason’s speed is 3.8 feet
per second.
U5-244
CCSS IP Support Supplement for Math II
5.6 Skill 5 Prerequisite Skills
© Walch Education