Math 2 Unit 2 examples

Tim Brzezinski, Katie Fay, Ramona Teodorescu, JoeVignolini, Oct 2, 2026

KPS Math 2 Unit 2 angles and lines

Table of Contents

  1. explore types of angles and names
    1. Math 2 - Review - Types of Angles
  2. More angle exploration
    1. Math 2 - Unit 2 - Angles
  3. Transversal Intersects Parallel Lines: Scenarios
    1. Transversal Intersects Parallel Lines
    2. Corresponding Angles and Parallel Lines
    3. Alternate Interior Angles and Parallel Lines
    4. Alternate Exterior Angles and Parallel Lines
    5. Same Side Interior Angles and Parallel Lines
    6. Same Side Exterior Angles and Parallel Lines
    7. Exploring Alternate Interior Angles (V2)
    8. Alternate Interior Angles Theorem (V3)
    9. Exploring Alternate Exterior Angles (V2)
    10. Alternate Exterior Angles Theorem (V3)
    11. Solution to Parallel Lines & Angles Problem
  4. Angle Position Names When Transversal Intersects Lines
    1. Naming Angle Positions
    2. Parallel Lines & Related Angles

1.

explore types of angles and names

  • 1. Math 2 - Review - Types of Angles

1.1.

Math 2 - Review - Types of Angles

[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][/size][/size]
Does line length affect the angle?
Try it: Use the applet and create the angle of the given size in each below.
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.
What type of angle?
What type of angle?
What type of angle?
– JoeVignolini, ewegner, My Geometry Resources

2.

More angle exploration

  • 1. Math 2 - Unit 2 - Angles

2.1.

Math 2 - Unit 2 - Angles

#1 and 2
#1) Find the midpoint of [math]\text{\overline{BC}}[/math]. Show the midpoint on the graph, and write the name and coordinates of the point.
#2) What is the midpoint of [math]\text{\overline{PQ}}[/math] given P(-2, 3p) and Q(4n, p)?
[size=150][color=#0000ff][b]RAY: [/b]A ray has one endpoint and extends indefinitely in one direction.[br][br][/color][/size][color=#0000ff][b]OPPOSITE RAYS: [/b]two rays with a common endpoint that form a straight line.[/color]
[size=150][color=#0000ff]An [b]ANGLE [/b]consists of two different rays with the same endpoint. The rays are SIDES and the endpoint is the VERTEX.[/color][/size]
#7) Use the applet! Drag my angle around.
#9
#8) Sometimes you will not see the entire rays that make the angle sides-- for example, if the angle is part of a triangle. In the applet, lengthen and shorten the segment sides of the angle-- do longer sides mean a larger angle?[br][br]Name this angle in 3 different ways.
[size=200][color=#0000ff]MEASURING ANGLES ON GEOGEBRA![/color][/size]
#9
#9) Measure the angle shown with the class, and then check your answer.[br]Now spend some time changing the angle, and measuring it. Be sure to measure small and large angles, and also to use both protractors.
[size=150][color=#0000ff][size=200]CLASSIFYING ANGLES[/size][/color][/size]
#10
#10) Write an equation involving the angles in the applet.
#11)
– Duane Habecker, JoeVignolini, cprystalski

3.

Transversal Intersects Parallel Lines: Scenarios

  • 1. Transversal Intersects Parallel Lines
  • 2. Corresponding Angles and Parallel Lines
  • 3. Alternate Interior Angles and Parallel Lines
  • 4. Alternate Exterior Angles and Parallel Lines
  • 5. Same Side Interior Angles and Parallel Lines
  • 6. Same Side Exterior Angles and Parallel Lines
  • 7. Exploring Alternate Interior Angles (V2)
  • 8. Alternate Interior Angles Theorem (V3)
  • 9. Exploring Alternate Exterior Angles (V2)
  • 10. Alternate Exterior Angles Theorem (V3)
  • 11. Solution to Parallel Lines & Angles Problem

3.1.

Transversal Intersects Parallel Lines

[b][color=#980000]Students:[/color][/b][br][br]Use the GeoGebra applet above to help you complete the [b][color=#1e84cc]Transversals, Lines, & Related Angles[/color][/b] investigation given to you at the beginning of class.
– Tim Brzezinski

3.2.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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4.

Angle Position Names When Transversal Intersects Lines

  • 1. Naming Angle Positions
  • 2. Parallel Lines & Related Angles

4.1.

Naming Angle Positions

Definition: A transversal is a line that intersects 2 other lines at 2 distinct points. [br][br]In the applet, the dashed line below is a transversal. (Actually, each of the three lines displayed below is a transversal.)[br][br]When a transversal intersects 2 other lines, special names are given to certain pairs of angles. [br]These angle pairs are called [b]corresponding angles, alternate interior angles, alternate exterior angles, same-side interior angles, and same-side exterior angles[/b]. [br][br]Explore these angle pairs within the applet below. Then, answer the questions that follow.
Questions:[br][br]1) What does the term "same-side" mean in the phrases "same-side interior angles" and "same-side exterior angles"? [br]2) What does the term "alternate" mean in the phrases "alternate interior angles" and "alternate exterior angles"? [br]3) Which of the four displayed angles would be considered "interior" angles? Why is this?[br]4) Which of the four displayed angles would be considered "exterior" angles? Why is this?[br]5) How would you describe, in your own words, what it means for a pair of angles to be described as "corresponding angles"?
– Tim Brzezinski

4.2.

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