Triangle Congruence Wright
1. HSG.CO.B.7
1. SAS - Exercise 1A
2. SSS: Exercise 1
3. SSS: Exercise 2
2. HSG.CO.B.8
1. SAS: Dynamic Proof!
2. SSS: Dynamically Illustrated
3. ASA Theorem?

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Triangle Congruence Wright

Tim Brzezinski, Aaron Dankman, cf_wright, Oct 1, 2021

Triangle Congruence Theorem Practice and Demonstration. Credit due to T Brzezinski (https://www.geogebra.org/tbrzezinski). His work on dynamic transformational geometry materials for high school courses has been, well, transformational.

HSG.CO.B.7
1. SAS - Exercise 1A
2. SSS: Exercise 1
3. SSS: Exercise 2
HSG.CO.B.8
1. SAS: Dynamic Proof!
2. SSS: Dynamically Illustrated
3. ASA Theorem?

Information

1.

HSG.CO.B.7

1. SAS - Exercise 1A
2. SSS: Exercise 1
3. SSS: Exercise 2

1.1.

SAS - Exercise 1A

In the applet below, use the tools of transformational geometry to informally demonstrate the SAS Triangle Theorem to be true. That is, use the tools of transformational geometry to map the yellow triangle onto the empty triangle. Before starting, feel free to adjust any aspect of the starting triangle (tilt, size of the included angle, and the positions of points A, B, and C). You can also use the black slider to change the position of the image (empty) triangle. Once you do start, it is recommended that you don't readjust these parameters.

Question:

Describe how you know the two triangle are congruent.

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– Tim Brzezinski

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1.3.

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2.

HSG.CO.B.8

1. SAS: Dynamic Proof!
2. SSS: Dynamically Illustrated
3. ASA Theorem?

2.1.

SAS: Dynamic Proof!

The SAS Triangle Congruence Theorem states that if 2 sides and their included angle of one triangle are congruent to 2 sides and their included angle of another triangle, then those triangles are congruent. The applet below uses transformational geometry to dynamically prove this very theorem. Interact with this applet below for a few minutes, then answer the questions that follow. As you do, feel free to move the BIG WHITE POINTS anywhere you'd like on the screen!

1) What geometry transformations did you observe in the applet above? List them. 2) What common trait do all these transformations (you listed in your response to (1)) have?