Grade 8 Congruence and Transformations
Students will be able to define congruence of line segments, triangles, and regular polygons. Students will be able to Transform (Translate, Rotate, and Reflect) geometric shapes, lines, and points precisely on a coordinate plane. Students will understand how to derive Transformations of congruent figures using Euclidean Geometry of circles and straight lines.
Table of Contents
- Plotting Points
- Plotting Points (x,y): Dynamic Illustration
- Quadrant Identification
- Rant Rant Rant Rant!
- Identifying Transformations
- Identify Transformation Type
- Practicing Translations
- Translations with a Vector
- Parallel Lines
- Parallel lines with transversal and angles
- Practicing Reflections
- Reflections
- Exploring Reflections on the Coordinate Plane
- Practicing Rotations
- Rotations Exploration
- Pythagoras Theorem
- Pythag
Plotting Points (x,y): Dynamic Illustration
[b][color=#000000]A COORDINATE is a NUMBER or a LETTER that indicates LOCATION. [/color][/b][color=#000000][br]Did you ever play Milton Bradley's game [/color][b][color=#000000]Battleship[/color][/b][color=#000000] as a kid? [br]If so, you dealt with coordinates! "A5" was either a "hit" or a "miss", right? [br]In this game, the "A" and the "5" are called coordinates. [br][br]Your mobile device can indicate your latitude and longitude. [br][b]LATITUDE and LONGITUDE[/b] are numbers that help tell a person his/her [b]LOCATION.[/b] [br]Thus, [b]LATITUDE and LONGITUDE[/b] are said to form a pair of [b]COORDINATES. [/b] [br] [br][/color]Note the coordinate plane below. [color=#0000ff]Press the [/color][color=#38761d]"New Example"[/color][color=#0000ff] button. After doing so press [/color][color=#bf9000]"Plot Point"[/color][color=#0000ff]. [br][/color]Be sure to watch the specific dynamics of how to plot a point correctly. Repeat the [b][color=#0000ff]colored step[/color][/b] above approximately 10 times. [color=#000000]Then, go to the link indicated below the applet. [/color]
[color=#000000]Once you're confident in your ability to plot a point given its coordintes, [url=https://www.geogebra.org/m/AbRPAY8V]click here[/url] to put into practice what you've just learned! [/color]
Identify Transformation Type
Transformation Types
Translation: Sliding an image[br][br]Rotation: Spinning an image around a fixed point[br][br]Reflection: Mirroring an image across a fixed line[br][br]Dilation: Scaling and image up or down in size (Sometimes called "Enlargement")
Translations with a Vector
Click on point E to move the vector to see how the position of the image changes with the vector.
Translations with a Vector
Reflections
Opposite Isometries
Any isometry that reverses the orientation of a triangle is called an [i]opposite isometry[/i]. When you read off the vertices of triangle ABC in cyclic order, they are read in a counterclockwise direction. When you read off the vertices of triangle A'B'C' in cyclic order, they are read in a clockwise direction.
[math]\sigma_m[/math] is the notation we will use for a reflection in line [i]m[/i]. [br]In the sketch below, we would write [math]\sigma_{DE}\left(A\right)=A'[/math].