Unit 7, Lesson 3
Nonadjacent Angles
Grade 7
Preparation
Lesson Narrative
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 use repeated reasoning to see that the vertical angles have equal measures (MP8).
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 students do not need to be able to give a formal geometric proof that vertical angles must have equal measures.
- Comprehend that 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.
Let’s look at angles that are not right next to one another.
Required Preparation
None
Vertical angles are opposite angles that share the same vertex. They are formed when two lines cross each other. Their angle measures are equal.
Angles and are vertical angles. If angle measures , then angle must also measure .
Angles and are another pair of vertical angles.