Alternate Interior Angles
5 min
Teacher Prep
Setup
Narrative
The purpose of this activity is for students to recall prior work with supplementary angles and to connect vertical angles and 180-degree rotations of intersecting lines. As students find the angle measures, listen to their conversations, specifically for the use of vocabulary such as “supplementary angles,” “vertical angles,” and “rotations.”
Launch
Provide access to geometry toolkits, including protractors and tracing paper. If needed, display the image from the problem and invite a student to state the name of the 30∘ angle (JGF). Consider tracing the segments from J to G, then G to F, as the angle is being named to help students visualize the naming convention for angles where the middle letter denotes the angle’s vertex.
Student Task
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Find the measure of angle JGH. Explain or show your reasoning.
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Find and label a second 30∘ angle in the diagram. Find and label an angle congruent to angle JGH.
Sample Response
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150∘. Sample response: In the diagram, the given 30∘ angle and angle JGH are supplementary, so they add up to 180∘.
-
See image
Activity Synthesis (Teacher Notes)
Display the image for all to see. Invite students to share their responses, adding onto the image as needed to help make clear student thinking.
If no students use supplementary angles or the property that a straight line is 180∘, ask students how they could determine the measure of angle JGH without a protractor. Highlight 2 supplementary angles, such as JGF and JGH, and write the term “supplementary” on the display near those angles. Highlight two vertical angles such as JGF and HGI and write the term “vertical angles” on the display.
Standards
- 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
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Alternate Interior Angles
5 min
Teacher Prep
Setup
Narrative
The purpose of this activity is for students to recall prior work with supplementary angles and to connect vertical angles and 180-degree rotations of intersecting lines. As students find the angle measures, listen to their conversations, specifically for the use of vocabulary such as “supplementary angles,” “vertical angles,” and “rotations.”
Launch
Provide access to geometry toolkits, including protractors and tracing paper. If needed, display the image from the problem and invite a student to state the name of the 30∘ angle (JGF). Consider tracing the segments from J to G, then G to F, as the angle is being named to help students visualize the naming convention for angles where the middle letter denotes the angle’s vertex.
Student Task
-
Find the measure of angle JGH. Explain or show your reasoning.
-
Find and label a second 30∘ angle in the diagram. Find and label an angle congruent to angle JGH.
Sample Response
-
150∘. Sample response: In the diagram, the given 30∘ angle and angle JGH are supplementary, so they add up to 180∘.
-
See image
Activity Synthesis (Teacher Notes)
Display the image for all to see. Invite students to share their responses, adding onto the image as needed to help make clear student thinking.
If no students use supplementary angles or the property that a straight line is 180∘, ask students how they could determine the measure of angle JGH without a protractor. Highlight 2 supplementary angles, such as JGF and JGH, and write the term “supplementary” on the display near those angles. Highlight two vertical angles such as JGF and HGI and write the term “vertical angles” on the display.
Standards
- 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.