Congruence and Rigid Transformations
- Zachary Duncan
Intro: What do we mean by corresponding parts
1. Properties of Congruence, under a Translation
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
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.
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
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
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?