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Triangle Congruence Book 1
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1. HSG.CO.B.7
- Proving Tri's Congruent (I)
- Proving Tri's Congruent (II)
- SAS - Exercise 1A
- SAS - Exercise 1B
- SAS - Exercise 2
- SAS - Exercise 3
- SSS: Exercise 1
- SSS: Exercise 2
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2. HSG.CO.B.8
- SAS: Dynamic Proof!
- Animation 136
- SSS: Dynamic Proof!
- SSS: Dynamically Illustrated
- Animation 138
- ASA Theorem?
- Animation 137
- SSA Theorem? Interactive
- Copy of Is "SSA" Legit? What Do You Think?
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Triangle Congruence Book 1
Tim Brzezinski, Aaron Dankman, Jan 31, 2017
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.
Table of Contents
- HSG.CO.B.7
- Proving Tri's Congruent (I)
- Proving Tri's Congruent (II)
- SAS - Exercise 1A
- SAS - Exercise 1B
- SAS - Exercise 2
- SAS - Exercise 3
- SSS: Exercise 1
- SSS: Exercise 2
- HSG.CO.B.8
- SAS: Dynamic Proof!
- Animation 136
- SSS: Dynamic Proof!
- SSS: Dynamically Illustrated
- Animation 138
- ASA Theorem?
- Animation 137
- SSA Theorem? Interactive
- Copy of Is "SSA" Legit? What Do You Think?
Proving Tri's Congruent (I)
Recall an isometry is a transformation that preserves distance.
Also recall that, by definition, 2 polygons are said to be congruent polygons if and only if one polygon can be mapped perfectly onto the other polygon using an isometry or a composition of two or more isometries.
Use the tools of GeoGebra to show, by definition, that the following two triangles are congruent.
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?
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1) Translation, Rotation
2) Translation and rotation are rigid transformations, and both are isometric. Therefore they preserve distance and always produce an image congruent to the pre-image upon which the transformation was performed.
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