Lesson 2.1.1 What is the relationship?
September 21, 2016
Lesson 2.1.1 What is the relationship?
Complementary, Supplementary, and Vertical Angles
Lesson Objective:
Students will be introduced to a problem about mirror reflections that will motivate much of their work in
Section 2.1. Students will learn how to name angles, and will learn the three main relationships for angle
measures, namely, supplementary, complementary, and same (have the same measure). Students will also
discover that vertical angles have the same measure.
CCSS Standard(s):
G-CO.9
Mathematical Practices:
In this lesson students will need to attend to precision when naming angles and finding relationships.
They will also need to justify their reasoning as they find the relationships of different angles.
Core Problems:
2?1 through 2?4
Materials:
?
Hinged mirrors, one per student (or pair of students) and one for teacher demonstration
Suggested Lesson Activity:
It is important that students finish problems 2?1 through 2?4 before moving to Lesson 2.1.2. Keep a
close eye on time during this lesson. The Team Roles section has some suggestions for ways to
handle confusion today so that teams do not get stuck or spend too much time on any one problem.
For an average class, follow the time suggestions below:
Problem 2?1
5 minutes
Continued next page
Problems 2?2 thru 2?4
30 mins
Problem 2?5
15 mins
September 21, 2016
This lesson could be done using Red Light Green Light.
2-1 Have a student volunteer read the directions for problem 2?1 for the class. Distribute hinged mirrors to
the students, one per student (or pair of students) and discuss the situation. Remember that this is just an
introduction to the context. There is nothing yet to ¡°solve.¡±
2-2
Move teams on to problem 2?2, which introduces the notation and convention used for naming angles.
2-3 - 2-4 Teams should continue to work on problems 2?3 and 2?4, which introduce three common
relationships between angle measures: complementary, supplementary, and same (have equal measure). This
begins the focus on external relationships that will continue throughout this chapter and the rest of this course.
2-5 if you have time, could be done using a Pairs Check, otherwise assign it with today's homework.
Students will often be confused between the different types of relationships. Help students recognize that many
angle pairs they will study have two types of relationships;
¨C a geometric relationship and an angle measure relationship.
For example, ?PML and ?PMN in the diagram at right have a geometric
relationship (they form a straight angle) and a relationship between their
angle measures (they are supplementary).
Another example is shown at right, where ?AED and ?CEB have a geometric
relationship (they are vertical angles) and an angle measure relationship
(their measures are equal).
Closure: Problem 2?7 asks students to record the angle relationships they learned about during this lesson in
their Learning Logs. This entry should include information about complementary, supplementary, same (have
equal measure), and vertical angles.
September 21, 2016
Homework Check: The answers are in your text.
Questions about specific problems?
You just made closure for Chapter 1 ... what might
you expect to see in the coming week?
September 21, 2016
September 21, 2016
2-1. SOMEBODY¡¯S WATCHING ME
In order to see yourself in a small mirror, you usually have to be looking directly into it
¡ªif
you move off to the side, you cannot see your image any more. But Mr. Douglas knows a
neat
trick. He claims that if he makes a right angle with a hinged mirror, he can see himself in the
mirror no matter from which direction he looks into it.
a.
By forming a right angle with a hinged mirror, test Mr. Douglas¡¯s trick for
yourself.
Look into the place where the sides of the mirror meet. Can you see yourself? What if
you
look in the mirror from a different angle?
b. Does the trick work for any angle between the sides
of the mirror? Change the angle between the sides
of the mirror until you can no longer see your reflection
where the sides meet.
c.
Below is a diagram of a student trying out the mirror
trick. What appears to be true about the lines of sight?
Can you explain why Mr. Douglas¡¯s trick works? Talk
about this with your team and be ready to share your
ideas with the class.
(Distribute Hinged
Mirrors)
CW:2-1to2-4
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