Triangle Congruence Book 1

Tim Brzezinski, Aaron Dankman, Jan 31, 2017

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

  1. HSG.CO.B.7
    1. Proving Tri's Congruent (I)
    2. Proving Tri's Congruent (II)
    3. SAS - Exercise 1A
    4. SAS - Exercise 1B
    5. SAS - Exercise 2
    6. SAS - Exercise 3
    7. SSS: Exercise 1
    8. SSS: Exercise 2
  2. HSG.CO.B.8
    1. SAS: Dynamic Proof!
    2. Animation 136
    3. SSS: Dynamic Proof!
    4. SSS: Dynamically Illustrated
    5. Animation 138
    6. ASA Theorem?
    7. Animation 137
    8. SSA Theorem? Interactive
    9. Copy of Is "SSA" Legit? What Do You Think?

1.

HSG.CO.B.7

  • 1. Proving Tri's Congruent (I)
  • 2. Proving Tri's Congruent (II)
  • 3. SAS - Exercise 1A
  • 4. SAS - Exercise 1B
  • 5. SAS - Exercise 2
  • 6. SAS - Exercise 3
  • 7. SSS: Exercise 1
  • 8. SSS: Exercise 2

1.1.

Proving Tri's Congruent (I)

[color=#000000]Recall an [b]isometry[/b] is a [b]transformation that preserves distance. [br][/b][br]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. [br][br]Use the tools of GeoGebra to show, by definition, that the following two triangles are congruent. [/color]
– Tim Brzezinski

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1.3.

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1.4.

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1.5.

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1.6.

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1.7.

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1.8.

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2.

HSG.CO.B.8

  • 1. SAS: Dynamic Proof!
  • 2. Animation 136
  • 3. SSS: Dynamic Proof!
  • 4. SSS: Dynamically Illustrated
  • 5. Animation 138
  • 6. ASA Theorem?
  • 7. Animation 137
  • 8. SSA Theorem? Interactive
  • 9. Copy of Is "SSA" Legit? What Do You Think?

2.1.

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?
– Aaron Dankman, Tim Brzezinski

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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