[b]Use the diagram above to complete the following exercises. [/b]
Exploring Angle Relationships and Angles in Triangles
Table of Contents
- Exploring Vertical Angles
- Exploring Vertical Angles
- Exploring Supplementary Angles
- Exploring Supplementary Angles
- Exploring Complementary Angles
- Exploring Complementary Angles
- Exploring Parallel Lines Cut by a Transveral
- Exploring Angle Relationships
- Exploring Triangle Angle Sum Theorem
- Explore Triangle Angle Sum Theorem
- Explore Exterior Angle of a Triangle
- Check and Review Worksheet
- Check and Review Worksheet
Exploring Vertical Angles
Vertical Angles
Use the applet below to answer the questions that appear beneath it.
Move the slider and examine the angle measures of the [b][color=#00ff00]green angle[/color][/b]. What do you notice?
Click the other checkbox to show the [b][color=#ff0000]other pair of vertical angles[/color][/b]. [br]Move the slider and examine the angle measures of the [b][color=#ff0000]two red vertical angles [/color][/b]now. [br]What do you notice?
Now that you have all four angle measures displayed, drag the slider around. What can you conclude about the relationship between vertical angles?
Exploring Supplementary Angles
Supplementary Angles
[size=200][size=100]Use the applet below to answer the questions that appear beneath it. [/size][/size]
1
Use the slider to adjust the measures of the [b][color=#ff00ff]pink[/color][/b] and [b][color=#0000ff]blue[/color][/b] angles. What do you notice about the [color=#ff00ff][b]pink[/b][/color] [b][color=#ff00ff]angle[/color][/b] as the [color=#0000ff][b]blue angle[/b][/color] increases?
2
In the applet above, the [b][color=#0000ff]blue angle[/color][/b] and the [b][color=#ff00ff]pink angle[/color][/b] are said to be [b]supplementary angles[/b]. Given this information, determine the supplement of a 55° angle.
3
What is the supplement of a 1-degree angle?
4
Do supplementary angles have to be adjacent? Explain your thinking.
5
In your own words, what are supplementary angles?
Exploring Complementary Angles
Complementary Angles
Use the applet below to answer the questions that appear beneath it.
1.
In your own words, describe what it means for 2 angles to be complementary angles.
2.
[color=#000000]In the applet above, the [/color][b][color=#0000ff]blue angle[/color][/b][color=#000000] is said to be a [/color][i][color=#000000][b]complement [/b][/color][/i][color=#000000]of the [/color][color=#ff00ff][b]pink angle[/b][/color][color=#000000], and vice versa.[br][/color][color=#000000]Given this information, determine the [/color][i][color=#000000]complement[/color] [/i][color=#000000]of a 40 degree angle. [br][/color]
3.
What is the complement of a 1-degree angle?
4.
What angle measure has a complement whose measure is equal to itself?
Exploring Angle Relationships
Parallel Lines Cut by a Transveral Line
Identify and list at least two pairs of corresponding angles. Then determine the relationship between corresponding angles.
Identify at least one pair of alternate interior angles. Then determine the relationship between alternate interior angles.
Identify at least one pair of alternate exterior angles. Then determine the relationship between alternate exterior angles.
Identify at least one pair of same-side interior angles. Then determine the relationship between same-side interior angles.
Explore Triangle Angle Sum Theorem
Triangle Angle sum
What do you notice about the sum of the three interior angles of the triangle?
Describe the relationship between one inteior angle of the triangle and its exterior angle.
Check and Review Worksheet
Go to your teacher and ask them for a copy of the Check and Review Worksheet once you have finished all of the other tasks.