Angle Congruence Theorems

Aaron Dankman, Nov 2, 2016

Review, exercises, and a fun challenge related to some angle theorems

Table of Contents

  1. Proving Theorems
    1. Defining Congruence
    2. Proving Congruence
    3. Proof: Vertical Angles Theorem
    4. Proof: Corresponding Angles Theorem
    5. Fun!
    6. Prove Angle Congruence
  2. Applying Theorems
    1. Part 1: Observe and Conjecture
    2. Part 2: Investigate
    3. Part 3: Prove

1.

Proving Theorems

  • 1. Defining Congruence
  • 2. Proving Congruence
  • 3. Proof: Vertical Angles Theorem
  • 4. Proof: Corresponding Angles Theorem
  • 5. Fun!
  • 6. Prove Angle Congruence

1.1.

Defining Congruence

What is true of the two angles below? Use a biconditional statement to explain how you know.
Click the "Check" box to evaluate the quality of your response.
– Aaron Dankman, Tim Brzezinski

1.2.

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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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2.

Applying Theorems

  • 1. Part 1: Observe and Conjecture
  • 2. Part 2: Investigate
  • 3. Part 3: Prove

2.1.

Part 1: Observe and Conjecture

[u]Observe[/u][br]Precisely and completely describe the relationship between line f and line f'.
Play with the applet below, then respond to the prompt that follows.
[u]Conjecture[br][/u]In geometry when we think something is true but haven't proven it yet, we call it a conjecture. [br][br]Consider angle AEA'. What do you think its relationship is to angle BAE and angle B'A'E? Write a conjecture.
– Aaron Dankman

2.2.

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2.3.

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Information