Relationships of Angles
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to bring back to mind what students have learned previously about angle measures, as well as to discuss what aspects of each figure tell us about an angle.
Listen for the language that students use as they compare the sizes of the angles in the first question and as they name the angles in the second question. Select students to share different ways of naming the same angle
Launch
Give students 1 minute of quiet work time, followed by a whole-class discussion.
Student Task
-
Which angle is bigger?
-
Identify an obtuse angle in the diagram.
Sample Response
- Sample response: Neither. Both angles have the same measure.
- Angle DAB (or angle BAD) is obtuse. It measures 110∘ because 60+50=110.
Activity Synthesis (Teacher Notes)
The goal of this discussion is to ensure that students understand that angles measure the amount of turn between two different directions.
Ask students to share how they decided whether Angle a and Angle b are the same or different sizes. If students do not agree that the angles are the same size, display this applet for all to see:
Demonstrate dragging one angle onto the other angle.
Display the applet or figure in the second question, and ask previously identified students to share their responses. Make sure students understand that saying angle A is not specific enough when referring to this diagram, because there is more than one angle with its vertex at point A.
Explain to the students that by using three points to refer to an angle, with the middle point being the vertex of the angle, we can be sure that others will understand which angle we are talking about. Have students practice this way of referring to angles by asking questions such as:
-
“Which angle is bigger, angle DAC or angle CAB?” (Angle DAC is bigger because its measure is 60 degrees. It doesn’t matter that segment BA is longer than segment DA.)
-
“Which angle is bigger, angle CAB or angle BAC?” (They are both the same size, because they are two names for the same angle.)
Also explain to students that in a diagram an arc is often placed between the two sides of the angle being referred to.
Tell students that angles DAC and CAB are known as adjacent angles because they are next to each other, sharing segment AC as one of their sides and A as their vertex.
Standards
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.5·Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
- 7.G.B.5·Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
15 min
10 min
Knowledge Components
All skills for this lesson
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Relationships of Angles
5 min
Teacher Prep
Setup
Narrative
The purpose of this Warm-up is to bring back to mind what students have learned previously about angle measures, as well as to discuss what aspects of each figure tell us about an angle.
Listen for the language that students use as they compare the sizes of the angles in the first question and as they name the angles in the second question. Select students to share different ways of naming the same angle
Launch
Give students 1 minute of quiet work time, followed by a whole-class discussion.
Student Task
-
Which angle is bigger?
-
Identify an obtuse angle in the diagram.
Sample Response
- Sample response: Neither. Both angles have the same measure.
- Angle DAB (or angle BAD) is obtuse. It measures 110∘ because 60+50=110.
Activity Synthesis (Teacher Notes)
The goal of this discussion is to ensure that students understand that angles measure the amount of turn between two different directions.
Ask students to share how they decided whether Angle a and Angle b are the same or different sizes. If students do not agree that the angles are the same size, display this applet for all to see:
Demonstrate dragging one angle onto the other angle.
Display the applet or figure in the second question, and ask previously identified students to share their responses. Make sure students understand that saying angle A is not specific enough when referring to this diagram, because there is more than one angle with its vertex at point A.
Explain to the students that by using three points to refer to an angle, with the middle point being the vertex of the angle, we can be sure that others will understand which angle we are talking about. Have students practice this way of referring to angles by asking questions such as:
-
“Which angle is bigger, angle DAC or angle CAB?” (Angle DAC is bigger because its measure is 60 degrees. It doesn’t matter that segment BA is longer than segment DA.)
-
“Which angle is bigger, angle CAB or angle BAC?” (They are both the same size, because they are two names for the same angle.)
Also explain to students that in a diagram an arc is often placed between the two sides of the angle being referred to.
Tell students that angles DAC and CAB are known as adjacent angles because they are next to each other, sharing segment AC as one of their sides and A as their vertex.
Standards
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.A·Draw, construct, and describe geometrical figures and describe the relationships between them.
- 7.G.5·Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
- 7.G.B.5·Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.