Geometry: Lesson 3.1 â Parallel Lines and Transversals
Geometry: Lesson 3.1 – Parallel Lines and Transversals Geometry Oklahoma Academic Standards:
G.2D.1.1 Apply the properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve real-world and mathematical problems and determine if two lines are parallel, using algebraic reasoning and proofs.
Lesson Objectives:
1. To recognize angle pairs in parallel lines with transversals. 2. To use angle pairs to solve problems.
Introduction: In the previous chapter, we looked at the ways line segments and angles relate to each other individually. In this chapter, we will explore relationships that angles have with lines collectively.
Vocabulary: Definition – Parallel Two lines are parallel if they never intersect in the same plane.
Some real world examples of parallel lines are __________________________________ and _______________________________.
If we were to take two parallel lines and intersect both of them with another line, that third line would be called a transversal line.
Vocabulary: Definition – Transversal A transversal is any line that passes through 2 or more other lines.
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In the real world, you could think of a transversal as being a road that intersected two other roads (like Highway 75 intersecting 6th and 7th streets, etc.).
When a transversal line intersects two parallel lines, it creates 8 angles. Here’s a diagram to demonstrate:
If we were to pair these angles together, we could create some interesting relationships. Vocabulary: Definition – Corresponding Angles Corresponding Angles share position.
In the diagram, these angle pairs are __________________________________________. Vocabulary: Definition –Exterior Angles Exterior Angles are on the outside of the parallel lines.
In the diagram, these angle pairs are __________________________________________. Vocabulary: Definition –Interior Angles Interior Angles are on the inside of the parallel lines.
In the diagram, these angle pairs are __________________________________________.
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Vocabulary: Definition – Consecutive Angles Consecutive Angles are on the same-side of the transversal line
In the diagram, these angles are ______________________________________________. Vocabulary: Definition –Alternate Angles Alternate Angles are on the opposite side of the transversal line
In the diagram, these angles are ______________________________________________.
You can also mix and match any of these words together. For example, what would be the Alternate Interior angle pairs?
________________________________________________________________________ What would be the Alternate Exterior angle pairs?
________________________________________________________________________ How about the Consecutive Interior angle pairs?
________________________________________________________________________ Obviously, we could make the picture become much more chaotic to process the angle relationships by adding more transversal lines (like a city road map).
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Here’s an example with two transversal lines:
a.) Name the relationship between angles 5 and 13.
_____________________________________________ b.) Name the relationship between angles 8 and 14.
_____________________________________________
c.) Name the relationship between angles 15 and 16. _____________________________________________ d.) Name the relationship between angles 1 and 7.
_____________________________________________
e.) Name the relationship between angles 12 and 14. _____________________________________________ f.) Name the relationship between angles 9 and 11.
_____________________________________________
g.) Name the relationship between angles 10 and 13. _____________________________________________
Assignment 3.1 You have the choice of the following:
1. Use a city map of Okmulgee to identify an example of each of the following angle pairs: Corresponding angles, Consecutive Interior Angles, Consecutive Exterior Angles, Alternate
Interior Angles, and Alternate Exterior Angles. Be sure to label your map, angles, and angle pairs.
2. Complete the handout, “Geometry: Handout 3.1” and turn it in.
Geometry: Lesson 3.1
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G.2D.1.1 Apply the properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve real-world and mathematical problems and determine if two lines are parallel, using algebraic reasoning and proofs.
Lesson Objectives:
1. To recognize angle pairs in parallel lines with transversals. 2. To use angle pairs to solve problems.
Introduction: In the previous chapter, we looked at the ways line segments and angles relate to each other individually. In this chapter, we will explore relationships that angles have with lines collectively.
Vocabulary: Definition – Parallel Two lines are parallel if they never intersect in the same plane.
Some real world examples of parallel lines are __________________________________ and _______________________________.
If we were to take two parallel lines and intersect both of them with another line, that third line would be called a transversal line.
Vocabulary: Definition – Transversal A transversal is any line that passes through 2 or more other lines.
Geometry: Lesson 3.1
1
In the real world, you could think of a transversal as being a road that intersected two other roads (like Highway 75 intersecting 6th and 7th streets, etc.).
When a transversal line intersects two parallel lines, it creates 8 angles. Here’s a diagram to demonstrate:
If we were to pair these angles together, we could create some interesting relationships. Vocabulary: Definition – Corresponding Angles Corresponding Angles share position.
In the diagram, these angle pairs are __________________________________________. Vocabulary: Definition –Exterior Angles Exterior Angles are on the outside of the parallel lines.
In the diagram, these angle pairs are __________________________________________. Vocabulary: Definition –Interior Angles Interior Angles are on the inside of the parallel lines.
In the diagram, these angle pairs are __________________________________________.
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Vocabulary: Definition – Consecutive Angles Consecutive Angles are on the same-side of the transversal line
In the diagram, these angles are ______________________________________________. Vocabulary: Definition –Alternate Angles Alternate Angles are on the opposite side of the transversal line
In the diagram, these angles are ______________________________________________.
You can also mix and match any of these words together. For example, what would be the Alternate Interior angle pairs?
________________________________________________________________________ What would be the Alternate Exterior angle pairs?
________________________________________________________________________ How about the Consecutive Interior angle pairs?
________________________________________________________________________ Obviously, we could make the picture become much more chaotic to process the angle relationships by adding more transversal lines (like a city road map).
Geometry: Lesson 3.1
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Here’s an example with two transversal lines:
a.) Name the relationship between angles 5 and 13.
_____________________________________________ b.) Name the relationship between angles 8 and 14.
_____________________________________________
c.) Name the relationship between angles 15 and 16. _____________________________________________ d.) Name the relationship between angles 1 and 7.
_____________________________________________
e.) Name the relationship between angles 12 and 14. _____________________________________________ f.) Name the relationship between angles 9 and 11.
_____________________________________________
g.) Name the relationship between angles 10 and 13. _____________________________________________
Assignment 3.1 You have the choice of the following:
1. Use a city map of Okmulgee to identify an example of each of the following angle pairs: Corresponding angles, Consecutive Interior Angles, Consecutive Exterior Angles, Alternate
Interior Angles, and Alternate Exterior Angles. Be sure to label your map, angles, and angle pairs.
2. Complete the handout, “Geometry: Handout 3.1” and turn it in.
Geometry: Lesson 3.1
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