Rigid Motions and Congruent Triangles Worksheets
This topic focuses on a simple lesson that if a figure undergoes a rigid motion both its original and ending form are congruent. That tells us that all the corresponding sides and angles of both figures are congruent as well. This page contains a series of wonderful worksheets and lessons that help you learn how to use motions with congruent shapes. We will work within the coordinate place, in most cases, to help us chart and track these movements. This topic will be paramount as students begin to write proofs.
Aligned Standard: High School Geometry - HSG-CO.B.7
- 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.
- Answer Keys - These are for all the unlocked materials above.
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).
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.
- Quiz 1 - S and T: Are they congruent?
- Quiz 2 - Map the movements of each shape.
- Quiz 3 - WXYZ and LMNO are the same size. Are the rectangles congruent?
What is Congruence of Figures That Undergo Rigid Motions?
We know what congruence is, right? Congruence is the ability of two figures to be 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 preserve their identity and be considered congruent.
In simple words, rigid motion moves figures to new locations without altering their shapes and sizes, while maintaining the conditions for the figures to be congruent. This simple point has a great deal of significance as we move towards writing and reading geometric proofs. That is because if we can identify two congruent shapes it tells us that all of their sides and angles are congruent as well. From this information we can better understand all the different aspects of other shapes that may occupy the same coordinate plane. It is important that you remember this material as you begin work with proofs.