# Congruence and Rigid Transformations

- Author:
- Zachary Duncan

## Intro: What do we mean by corresponding parts

## 1. Properties of Congruence, under a Translation

## a.

Translate quadrilateral *ABCD* from point *C* to point *V.*
*Select the vector tool , and draw a vector starting at point *C* and ending at point *V*. Then, select the translate by vector tool , click on quadrilateral *ABCD*, and then click on the vector.
***If you need help, watch this video on how to do a Translation**

## b.

After you have translated quadrilateral *ABCD*, select the angle tool , and measure all four interior angles on the pre-image and image. **What do you notice about every pair of corresponding angles?**
***Video help on how to Measure Angles. **

## c.

Now, grab the distance measuring tool, , and measure all four side lengths on both the pre-image and the image. **What do you notice about every pair of corresponding sides?**
***Video help on how to Measure Side Lengths. **

## 2. Properties of congruence, under a reflection

## a. Reflect triangle DEF over line m

***Video help on how to do a Reflection.**

## b.

Just like in question 1, measure all interior angles and all side-lengths on both the pre-image (triangle DEF) and the image (triangle D'E'F'). **What do you notice about pairs of corresponding sides and angles?**

## 3. Properties of congruence, under a rotation.

## a. Rotate triangle JKL 180 degrees using V as the center of rotation

***Video help on how to do a Rotation.**

## b.

Just like in question 2, measure all pairs of corresponding sides and interior angles.
**Based on our work in questions 1-3, what can we conclude about corresponding sides and angles under one or more rigid transformations?**

## Summary of questions 1-3

**Corresponding Parts:**Corresponding sides and angles are a pair of matching angles or sides that are in the same spot in two different shapes. The shapes must either be similar or congruent. A

**rigid transformation**is a transformation for which all pairs of corresponding lengths and angle measures in the original figure and its image are equal. Translations, rotations, and reflections have this property, so they are rigid transformations.