Triangle Congruence Theorems 1

Tim Brzezinski, Aaron Dankman, Jan 31, 2017

[b]This GeoGebra Book contains lots of discovery-based learning activities, investigations, and meaningful remediation worksheets that were designed to help enhance students' learning of geometry concepts both inside and outside of the mathematics classroom. [color=#1551b5]This GeoGebra Book also contains contributions from the following individuals: Jennifer Silverman ([url]https://www.geogebra.org/jennifer+silverman[/url]) Steve Phelps ([url]https://www.geogebra.org/stevephelps[/url]) Dr. Ted Coe ([url]https://www.geogebra.org/tedcoe[/url]) Without their amazing talent and creativity, this resource would not have been possible. [/b][/color]

Table of Contents

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

1.

HSG.CO.B.8

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

1.1.

ASA Theorem?

[color=#000000]Suppose 2 triangles have 2 pairs of congruent angles. Suppose we also know that the side between each set of given angles (in one triangle) is congruent to the side between this same pair of angles in the other triangle. [br][br]Does knowing only this constitute sufficient evidence to prove the triangles congruent? If so, explain how/why with respect to the transformations and/or triangle congruence theorems you've previously learned. If not, clearly explain why not. [/color]
Quick (Silent) Demo
– Tim Brzezinski

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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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1.9.

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2.

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
  • 9. SSS: Exercise 3

2.1.

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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2.7.

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2.8.

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2.9.

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