Triangle Congruence Wright
Triangle Congruence Theorem Practice and Demonstration. Credit due to T Brzezinski ([url]https://www.geogebra.org/tbrzezinski[/url]). His work on dynamic transformational geometry materials for high school courses has been, well, transformational.
Table of Contents
- HSG.CO.B.7
- SAS - Exercise 1A
- SSS: Exercise 1
- SSS: Exercise 2
- HSG.CO.B.8
- SAS: Dynamic Proof!
- SSS: Dynamically Illustrated
- ASA Theorem?
SAS - Exercise 1A
In the applet below, use the tools of transformational geometry to informally demonstrate the SAS Triangle Theorem to be true. [br][br]That is, use the tools of transformational geometry to map the [color=#bf9000][b]yellow triangle[/b][/color] onto the empty triangle. [br][br]Before starting, feel free to adjust any aspect of the [color=#bf9000][b]starting triangle[/b][/color] ([color=#666666][b]tilt[/b][/color], [color=#1e84cc][b]size of the included angle[/b][/color], [b]and the positions of points [/b][i]A[/i][b], [/b][i]B[/i][b], and [/b][i]C[/i]). You can also use the [b]black slider[/b] to [b]change the position of the image (empty) triangle.[/b] [br][br][i]Once you do start, it is recommended that you don't readjust these parameters. [/i]
Question:
Describe how you know the two triangle are congruent.
SAS: Dynamic Proof!
[color=#000000]The [/color][b][u][color=#0000ff]SAS Triangle Congruence Theorem[/color][/u][/b][color=#000000] states that [/color][b][color=#000000]if 2 sides [/color][color=#000000]and their [/color][color=#ff00ff]included angle [/color][color=#000000]of one triangle are congruent to 2 sides and their [/color][color=#ff00ff]included angle [/color][color=#000000]of another triangle, then those triangles are congruent. [/color][/b][color=#000000]The applet below uses transformational geometry to dynamically prove this very theorem. [br][br][/color][color=#000000]Interact with this applet below for a few minutes, then answer the questions that follow. [br][/color][color=#000000]As you do, feel free to move the [b]BIG WHITE POINTS[/b] anywhere you'd like on the screen! [/color]
1) What geometry transformations did you observe in the applet above? List them. [br]2) What common trait do all these transformations (you listed in your response to (1)) have?