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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