Points, Lines, Planes, and Angles

Jason Wofsey, Amanda Purelli, May 21, 2019

Table of Contents

  1. Naming Figures
    1. Naming Figure 1
    2. Naming Figure 2
    3. Naming Figure 3
  2. Definitions
    1. Congruent Segments: Quick Exploration
    2. Midpoint Definition
    3. Segment Bisector Definition
    4. Collinear Points (Definition Prompt)
  3. Postulates
    1. Segment Addition Postulate
    2. Angle Addition Postulate
    3. Postulate 5
    4. Postulate 6
    5. Postulate 7
    6. Postulate 8
    7. Postulate 9
  4. Theorems
    1. Theorem 1-1
    2. Theorem 1-2
    3. Theorem 1-3
  5. Planes
    1. Intersecting Planes
    2. Rectangular Prism
    3. Line Intersecting Plane
    4. Square Pyramid Color
    5. Rectangular Prism 2
    6. Isosceles Triangular Prism
  6. Angles
    1. Protractor
    2. Congruent Angles: Definition
    3. Angle Bisector Definition (I)
    4. AAP - Problem 1 (Discovery)
    5. AAP - Problem 2
    6. AAP - Problem 3
    7. Angle Bisector (Problem 1)
  7. Exercises
    1. SAP Problem 1 (Discovery)
    2. SAP - Problem 2
    3. SAP - Problem 3
    4. Midpoint Definition Question (I)
    5. Midpoint Definition Question (II)

1.

Naming Figures

  • 1. Naming Figure 1
  • 2. Naming Figure 2
  • 3. Naming Figure 3

1.1.

Naming Figure 1

Write the letters in the box and choose the symbol from the dropdown menu.
– Jason Wofsey

1.2.

–

1.3.

–

2.

Definitions

  • 1. Congruent Segments: Quick Exploration
  • 2. Midpoint Definition
  • 3. Segment Bisector Definition
  • 4. Collinear Points (Definition Prompt)

2.1.

Congruent Segments: Quick Exploration

[color=#000000]The following app illustrates what it means for segments to be classified as [b]congruent segments.  [br][/b][/color]
Interact with the applet below for a few minutes. Be sure to move the LARGE POINTS around each time before you drag the slider! Then answer the questions that follow.
What transformations have we learned about so far? List them.
What transformations did you observe here while interacting with this app?
What does it mean for segments to be classified as [b]congruent segments[/b]? Explain.
– Tim Brzezinski

2.2.

–

2.3.

–

2.4.

–

3.

Postulates

  • 1. Segment Addition Postulate
  • 2. Angle Addition Postulate
  • 3. Postulate 5
  • 4. Postulate 6
  • 5. Postulate 7
  • 6. Postulate 8
  • 7. Postulate 9

3.1.

Segment Addition Postulate

– Jason Wofsey

3.2.

–

3.3.

–

3.4.

–

3.5.

–

3.6.

–

3.7.

–

4.

Theorems

  • 1. Theorem 1-1
  • 2. Theorem 1-2
  • 3. Theorem 1-3

4.1.

Theorem 1-1

– Jason Wofsey

4.2.

–

4.3.

–

5.

Planes

  • 1. Intersecting Planes
  • 2. Rectangular Prism
  • 3. Line Intersecting Plane
  • 4. Square Pyramid Color
  • 5. Rectangular Prism 2
  • 6. Isosceles Triangular Prism

5.1.

Intersecting Planes

– Jason Wofsey

5.2.

–

5.3.

–

5.4.

–

5.5.

–

5.6.

–

6.

Angles

  • 1. Protractor
  • 2. Congruent Angles: Definition
  • 3. Angle Bisector Definition (I)
  • 4. AAP - Problem 1 (Discovery)
  • 5. AAP - Problem 2
  • 6. AAP - Problem 3
  • 7. Angle Bisector (Problem 1)

6.1.

Protractor

Drag the blue point to move the protractor and the red point to rotate.
– Jason Wofsey

6.2.

–

6.3.

–

6.4.

–

6.5.

–

6.6.

–

6.7.

–

7.

Exercises

  • 1. SAP Problem 1 (Discovery)
  • 2. SAP - Problem 2
  • 3. SAP - Problem 3
  • 4. Midpoint Definition Question (I)
  • 5. Midpoint Definition Question (II)

7.1.

SAP Problem 1 (Discovery)

The questions you need to answer will appear in the applet below. So get started!
– Tim Brzezinski

7.2.

–

7.3.

–

7.4.

–

7.5.

–

Information