Understanding Rigid Transformations in Geometry
Explore the concept of rigid transformations in geometry, focusing on translation, rotation, and reflection. This guide explains how shapes can change position without altering their size or shape, distinguishing between preimages and images through notation. Learn how to identify and notate various transformations, including glide reflections. Engage with summaries, examples, and an interactive game to deepen your understanding of geometrical movement and relationships. Perfect for learners seeking to grasp the fundamentals of motion in geometry.
Understanding Rigid Transformations in Geometry
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Presentation Transcript
Rigid Transformations • Transformations that do not change shape or size. • Preimageis the original shape • Image is the shape that undergoes a transformation preimage image
NOTATION Many times the vertices are labeled. We’ll call this shape ABCDEFG B’ C’ C B D’ D This is the PREIMAGE A A’ E’ E When the pre-image is transformed, (rotated, translated, or reflected) it becomes: A’B’C’D’E’F’G’ The image of each vertex has a small tick mark. We say ‘prime’ every time we see one of them. This notation allows us to know which is the image and which is the pre-image – which, since they are rigid – are 2 identical figures. G’ G F F’ This is the IMAGE
A little extra, free information If we started with pre-image H and it was transformed, then the image would be H’. H H’
Hang in there M C L B P N A O E D ABCDE LMNOP
Transformations • There are 3 types of rigid transformations: • Translation – shapes slide along a straight path • Rotation – shapes turn about a point • Reflection – shapes flip across a line Hello. Hello.
Translation • Shapes slide • Every point of a figure moves in a straight line, all points move the same distance and same direction.
Rotation • Rotations turn • Every point of a figure moves around a given point called the center of rotation.
Reflection Reflections flip. • In a reflection, a line plays the role of a mirror. Every point in a figure is ‘flipped’ across the line. Glide Reflection
Glide Reflection This refers to a shape that is translated and reflected… like footprints on a beach.
Summary • What is the movement of a rotation? • What does is ‘turn’ around? • What is the movement of a translation? • What does it ‘slide’ on? • What is the movement of a reflection? • What does it ‘flip’ over? • When can the pre-image and the image be a different size? • How do you notate the pre-image? (For instance segment AB) • How do you notate the image?
Summary… part 2 • If I referred to the image M’, would that be the image or preimage? • Give an example of a rotation. • Give an example of a translation. • Give an example of a reflection. • Give an example of a glide reflection. • What is the conditional of ‘my mom is beautiful’? • What is the truth value? • What is the converse of ‘my mom is beautiful’? • What is the truth value? • Are you able to write a biconditional?
Game of War • Get a partner, a pencil and one piece of paper. • Fold the paper hamburger • With a straight edge, trace the fold • On your side, put 5 war things no bigger than a dime. Don’t group them together, spread them out. • Try and hit the other person’s items by drawing a bomb on your side, folding the paper and tracing the bomb.
BONUS!!!! • I’m looking for two things….. • Tell me the relationship between the pre-image of the bomb and the image of the bomb with the fold line. • Tell me the relationship between a segment drawn between the pre-image and image of a bomb with the fold line.
Assignment Motion in Geometry packet
