# Lesson 1

Rigid Transformations in the Plane

### Lesson Narrative

This lesson connects ideas from several previous units and extends them to the coordinate plane. In grade 8, students applied the Pythagorean Theorem to find the distance between two points in a coordinate system. Here, students calculate side lengths and angle measures, proving triangles are congruent. Students also draw and specify sequences of rigid transformations in the plane.

Each of these skills is a review, but the addition of the coordinate plane is novel. The goal is to prepare students to see transformations as functions using a new coordinate transformation notation that they will encounter in upcoming lessons. The notion of using the Pythagorean Theorem to calculate distances is a foundational idea that will reoccur in several lessons.

As students explore these ideas they discover the structure provided by a coordinate grid (MP7). Students learn to use this structure as well as impose their own by drawing auxiliary lines or right triangles to calculate lengths of segments.

Technology isn’t required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.

### Learning Goals

Teacher Facing

• Prove triangles are congruent using coordinates.
• Use the structure of the coordinate plane to perform reflections, rotations, and translations.

### Student Facing

• Let’s try transformations with coordinates.

### Required Preparation

Dynamic geometry software can be used in the Transforming by Coordinates activity, the cool-down, and the lesson synthesis. If that is not available, provide access to the geometry toolkits for tracing paper and straight edges.

Graph paper may be helpful to students in the lesson synthesis.

### Student Facing

• I can prove triangles are congruent using coordinates.
• I can reflect, rotate, and translate figures in the coordinate plane.

Building On