In this lesson, students see that angles do not need to be adjacent to be complementary or supplementary. Students are also introduced to and begin to use the term vertical angles for describing the opposite angles formed when two lines cross (MP6). They examine multiple examples and see that the vertical angles have equal measures. Students can relate this understanding to the fact that both angles in a pair of vertical angles are supplementary to the same angle in between, but in grade 7 students do not need to be able to give a formal geometric proof that vertical angles must have equal measures. As students see different ways of making pairs of supplementary angles in two lines crossing, they engage in MP7.
Lesson overview
- 3.1 Warm-up: Finding Related Statements (5 minutes)
- 3.2 Activity: Polygon Angles (10 minutes)
- 3.3 Activity: Vertical Angles (15 minutes)
- 3.4 Optional Activity: Row Game: Angles (10 minutes)
- Lesson Synthesis
- 3.5 Cool-down: Finding Angle Pairs (5 minutes)
Learning goals:
- Comprehend the term “vertical angles” (in spoken and written language) refers to a pair of angles created by two intersecting lines.
- Generalize (orally and in writing) that the opposite angles created by two intersecting lines have equal angle measures.
- Use reasoning about angle measures to identify complementary or supplementary angles that are not adjacent.
Learning goals (student facing):
- Let’s look at angles that are not right next to one another.
Learning targets (student facing):
- I can determine if angles that are not adjacent are complementary or supplementary.
- I can explain what vertical angles are in my own words.
Required materials:
- geometry toolkits
Glossary:
- vertical angles - Vertical angles are opposite angles that share the same vertex. They are formed by a pair of intersecting lines. Their angle measures are equal. For example, angles \(AEC\) and \(DEB\) are vertical angles. If angle \(AEC\) measures \(120^\circ\), then angle \(DEB\) must also measure \(120^\circ\). Angles \(AED\) and \(BEC\) are another pair of vertical angles.
- Access the complete Grade 7 glossary.
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.
This site includes public domain images or openly licensed images that are copyrighted by their respective owners. Openly licensed images remain under the terms of their respective licenses.