Unit 1, Lesson 8
Moves in Parallel
Accelerated 7
Preparation
Lesson Narrative
The focus of this lesson is for students to observe the effects of rigid transformations on lines and parallel lines. Parallel lines do not meet and are the same distance apart along their entire length, and a rigid transformation does not change these features. Students use the structure of parallel lines to conclude that the image of a set of parallel lines is also a set of parallel lines under a rigid transformation (MP7).
Students also investigate 180-degree rotations of points on a line and a set of intersecting lines. Students use arguments about 180-degree rotations to justify that vertical angles have the same measure (MP3).
This lesson is the first time students see the term “vertical angles” in this course. Students learn that vertical angles are two angles with the same measure formed by two intersecting lines, and they use transformations to understand why these pairs of angles have the same measure. If students need additional practice identifying vertical angles, use the Lesson Synthesis to display this image and ask students to identify four pairs of vertical angles. In particular, students may have trouble seeing that angles and are vertical angles.
- Draw and label rigid transformations of lines and parallel lines and explain (orally and in writing) the relationship between the original and its image under the transformation.
- Generalize that a rotation by 180 degrees about a point of two intersecting lines moves each angle to the angle that is vertical to it.
- Justify (orally) that vertical angles are congruent using informal arguments about 180-degree rotations of lines.
Let’s transform some lines.
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.