## Rigid Motions and Congruent Triangles

#### Aligned To Common Core Standard:

**High School Congruence** - HSG-CO.B.7

What is Congruence in Terms of Rigid Motions? We know what congruence is, right? Congruence is the ability of two figures being exactly the same or identical to each other. Congruent figures have the same size and shape. Now let's take a look at what rigid motions are. A series of transformations that do not change the size or shape of the figure is known as rigid motions. Rotations, reflections, and translations are considered rigid motions. If one figure can transform into another through rigid motion, the figures will be known as congruent. In simple words, rigid motion moves figures to new locations without altering their shapes and sizes, maintaining the conditions for the figures to be congruent. A series of wonderful worksheets and lessons that help you learn how to use motions with congruent shapes.

### Printable Worksheets And Lessons

- Congruence Defined
Step-by-step Lesson - Are the two triangles congruent based
on the definition of congruence?

- Guided Lesson
- See if you can prove the congruence between quadrilaterals, triangles,
and circles.

- Guided Lesson Explanation
- Some of these are straight yes or no questions. The remaining
questions require a bit of explaining.

- Practice Worksheet
- I could barely fit two graphs to a page to make them readable.

- Matching Worksheet
- Find all the coordinates that they are looking for here.

#### Homework Sheets

Reflections and deciding if triangles are congruent based on coordinates.

- Homework 1 - You can map triangle ABC to triangle STR by a reflection followed by a translation. Provide the coordinate notation for each.
- Homework 2 - The triangles are also two different sizes, so they are not congruent.
- Homework 3 - We can see that all points are moved (translated) 8 units left (x) and 12 units down (y).

#### Practice Worksheets

The first two sheets focus on determining congruency. The final sheet focuses on naming the movement of a translation.

- Practice 1 - ABCD and PQRS have different sizes. Since rigid motions preserve size, there is no sequence of rigid motions that will map ABCD to PQRS. Are the rectangles congruent?
- Practice 2 - EFGH and JKLM have different sizes. Since rigid motions preserve size, there is no sequence of rigid motions that will map EFGH to JKLM. Are the parallelograms congruent?
- Practice 3 - Provide the coordinate notation of the movements.

#### Math Skill Quizzes

We only ask you to identify a single part of each expression in the quizzes.