Dynamic Angles

William Sherlock Scott Holmes, Dec 15, 2025

Math

Table of Contents

  1. Points, Lines, Intervals and angles
    1. Points, Lines, Segments, and Rays
  2. Classifying Angles
    1. Types of Angles
    2. Copy of Angle Types
  3. Adjacent Angles
    1. Adjacent Angles
    2. Alternate Angles
  4. Complementary Angles
    1. Circle Geometry--Complimentary Angles
  5. Supplimentary Angles
    1. Supplementary Angles
  6. Angles in a revolution
    1. Three Ray Revolution - Angles at a point
  7. Corresponding angles
    1. Corresponding Angles
  8. Alternate angles
    1. Interior Alternate Angles
  9. Cointerior angles
    1. Cointerior Angles
  10. Vertically opposite angles
    1. Vertically Opposite Angles

1.

Points, Lines, Intervals and angles

  • 1. Points, Lines, Segments, and Rays

1.1.

Points, Lines, Segments, and Rays

This applet can be used to demonstrate the basic definitions and symbolic representations for lines, rays, segments, and points.
Why are there 2 sets of names/symbols for Rays?
– M Trivedi, Mathguru, Brian Connor

2.

Classifying Angles

  • 1. Types of Angles
  • 2. Copy of Angle Types

2.1.

Types of Angles

Instructions:
[size=200][size=150]Different types of angles have their own names.[br]Use the diagram to find the names of the five angle types.[br]Answer the questions below.[br][/size][/size]
Does line length affect the angle?
Try it:
An angle measures [math]\angle83^\circ[/math].  What type of angle is it?
An angle measures [math]\angle197^\circ[/math].  What type of angle is it?
An angle measures [math]\angle90^\circ[/math].  What type of angle is it?
An angle measures [math]\angle149^\circ[/math].  What type of angle is it?
Identify the types of angles below.
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What type of angle?
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What type of angle?
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What type of angle?
– Jianbender, ewegner, My Geometry Resources

2.2.

–

3.

Adjacent Angles

  • 1. Adjacent Angles
  • 2. Alternate Angles

3.1.

Adjacent Angles

Angles on opposite sides of a common arm are called adjacent angles.[br][i]AD[/i] is the common arm.
Adjacent Angles
Play around with the angles by dragging the blue dots. Move each dot at least once.
Adjacent Angles
What do you notice about the angles?
– Suzanne Schultz, Simon Job

3.2.

–

4.

Complementary Angles

  • 1. Circle Geometry--Complimentary Angles

4.1.

Circle Geometry--Complimentary Angles

Circle Geometry--Complimentary Angles
Circle Geometry--Complimentary Angles
Circle Geometry--Complimentary Angles
– Laura Brake

5.

Supplimentary Angles

  • 1. Supplementary Angles

5.1.

Supplementary Angles

Amulya B
[b]Supplementary Angles [/b]
Supplementary Angles
– Amulya B, Lepressley

6.

Angles in a revolution

  • 1. Three Ray Revolution - Angles at a point

6.1.

Three Ray Revolution - Angles at a point

When you have more than two angles in a revolution, each of the angles adds to 360[math]^\circ[/math]. In the example below, you can adjust [math]\angle[/math]ABC (also angle [math]\beta[/math] in the slider). Author's note: if you make this angle more than 280[math]^\circ[/math], things start to get a little messy. Notice that all three angles add up to 360[math]^\circ[/math].[br][br]When more than two angles share a vertex, it is called "angles at a point".
– Ryan Smith

7.

Corresponding angles

  • 1. Corresponding Angles

7.1.

Corresponding Angles

Corresponding Angles
Lines AB and FC are parallel. Line BC is a transversal.
Corresponding Angles
1. Use points A, B, and C to move the lines. Observe the angle values.
What do you observe about the angles?
We called these angles CORRESPONDING ANGLES.
How to identify corresponding angles?
One way to identify corresponding angles is to look for the letter F. Use the highlighter function to highlight the letter F.
Which of the following is correct?
Study the diagram below and answer the following question.
AB and CD are parallel lines and EH is a transversal.[br]What is the size of angle BFG?
Study the diagram below and answer the following question.
AB and CD are parallel lines and EH is a transversal.[br]What is the size of angle DGH?
In conclusion, we can say that corresponding angles are ................
– msgraceteo, GeoGebra Materials Team

8.

Alternate angles

  • 1. Interior Alternate Angles

8.1.

Interior Alternate Angles

Alternate interior angles are on the ____ ____ of the transversal.
True or False: Alternate interior angles have equal measures.
Graphics 1
[b][color=#ff0000][size=150]Use the image in Graphics 1 to answer the following questions:[/size][/color][/b]
Which pairs of angles are alternate interior angles?
Which angles would be congruent because they are alternate interior angles?
Alternate Exterior Angles
Alternate exterior angles are on the _____ ______ of the transversal
True or False: Alternate exterior angles have equal measures.
Which pair of angles are alternate exterior angles?
Is angle 8 measures 120 degrees, according to the alternate exterior angle rule, what other angle will measure 120 degrees?
– Judith Hilinski

9.

Cointerior angles

  • 1. Cointerior Angles

9.1.

Cointerior Angles

Cointerior angles on parallel lines.
Cointerior Angles
– Simon Job

10.

Vertically opposite angles

  • 1. Vertically Opposite Angles

10.1.

Vertically Opposite Angles

Vertically opposite angles are equal.
– Simon Job

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