1Vertical Angles and Parallel Lines
On the GED^{®} Mathematics Test, students may encounter questions that require them to integrate their understanding of lines, angles, and angle relationships.
 Students will need to recognize that when two straight lines intersect, they form two pairs of congruent angles, and that the angles opposite from each other are called vertical angles.
 Also, they will need to see that when two parallel lines are crossed by a transversal line, corresponding angles have the same measure.
This lesson is the basis for understanding the relationship between these angles when depicted in line drawings.
Students may become confused by the number of lines or angles in a drawing. It is essential to help them focus on what the question is asking and to use logical reasoning to work through the solution
Note: On the GED Mathematics Test, students will apply their understanding of angle concepts. They will not be asked to produce answers that require recall of terminology.
2Vertical Angles
Watch the video for an explanation of how congruent angles are formed when two lines intersect.
Angles: Vertical and Congruent
Video: 1m 25s
 Intersecting lines cross at some point, and when they cross, they create four angles. The angles opposite each other are called vertical angles.
 Vertical angles are congruent angles. This means they have the same measure.
Question In the diagram to the left, the lines JK and LM form vertical angles. The measure of ∠2 is 55°.
Find the measures of the remaining angles.
Step 1 Use supplementary angles to find the measure of ∠1. Since ∠1 + ∠2 = 180°, subtract 55° from 180° to find ∠1.
180° – 55° = 125°, so ∠1 = 125°.
Step 2 Use vertical angles to find the measure of ∠3.
∠3 = ∠1, so ∠3 = 125°.
Step 3 Use vertical angles to find the measure of ∠4.
∠4 = ∠2, which was given, so ∠4 = 55°.
Answer∠1 = 125°, ∠3 = 125°, ∠4 = 55°
3Parallel Lines Crossed by a Transversal
Watch the video for demonstration of the relationship between angles when parallel lines are crossed by a transversal.
Angles: Parallel Lines Crossed by a Transversal
Video: 1m 10s
 When two parallel lines are crossed by a third line, the crossing line is a transversal. The transversal creates four angles at each intersection.
 Two angles in the same position at each intersection are called corresponding angles. Corresponding angles have the same measure.
Question In the diagram to the left, lines m and n are parallel. They are crossed by transversal t. The measure of ∠1 is 110°.
Find the measures of the remaining angles.
Step 1 Use supplementary angles to find ∠2. Since ∠1 + ∠2 = 180°, subtract 110° from 180° to find ∠2.
180° – 110° = 70°, so ∠2 = 70°.
Step 2 Use vertical angles. Use given ∠1 and also ∠2.
∠1 = ∠4, so ∠4 = 110°.
∠2 = ∠3, so ∠3 = 70°.
Step 3 Use corresponding angles to find the remaining angles.
∠1 = ∠5, so ∠5 = 110°. ∠2 = ∠6, so ∠6 = 70°.
∠3 = ∠7, so ∠7 = 70°. ∠4 = ∠8, so ∠8 = 110°.
Answer Angles 4, 5, 8 = 110°. Angles 2, 3, 6, 7 = 70°.
4Sample GED Questions
Directions: There are two questions on this page. Each will appear in the blue rectangle below. Click on Question 1 to see the first question, and then select your answer. Click on Question 2 to see the second question, and select your answer. As you solve these problems, consider how you would work through them with your students.
Questions 1 and 2 are based on the following information and diagram.
How could you help students to focus on the information they need and ignore the information they don’t need to solve the problems?
Click for more teaching ideas.
5Skill Review
Lines, Angles, and Triangles: Vertical Angles and Parallel Lines Skill Review
Document
Printable Resource
In this lesson you have learned about vertical angles and parallel lines. This review consists of key terms and concepts with which you will need to be familiar. Click the view button on the left to access a review sheet.
Below you will also see a Classroom Connection with suggestions for linking this geometry content with your instruction.
Return to the GED Online Professional Development Course.
Credits
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Producer/Director: Vince Spoelker
Editor: Jim Piston
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Producer/Director: Vince Spoelker
Editor: Jim Piston
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Flash Programming: Dave Hamon
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PDF Layout Design: Amanda Dawahare
Vertical Angles and Parallel Lines Crossed by a Transversal is the fourth of eight selfpaced lessons in the “Lines, Angles, and Triangles” section of ...
Vertical Angles and Parallel Lines Crossed by a Transversal is the fourth of eight selfpaced lessons in the “Lines, Angles, and Triangles” section of KET’s GED^{®} Geometry Professional Development Online Course. Vertical Angles and Parallel Lines Crossed by a Transversal establishes the basis for understanding the relationship between vertical and congruent angles when depicted in line drawings.
Head Start Child Development and Early Learning Framework

3 (Prekindergarten ): The understanding of shapes, their properties, and how objects are related to one another.
Common Core State Standards

CCSS.Math.Con.HSGCO (High School  Geometry ): Congruence

CCSS.Math.Con.HSGCO.C (High School  Geometry ): Prove geometric theorems

CCSS.Math.Con.HSGCO.C (High School  Geometry ): Prove geometric theorems

CCSS.Math.Con.HSGSRT (High School  Geometry ): Similarity, Right Triangles, and Trigonometry

CCSS.Math.Con.HSGSRT.B (High School  Geometry ): Prove theorems involving similarity

CCSS.Math.Con.HSGSRT.B (High School  Geometry ): Prove theorems involving similarity

CCSS.Math.Cont.5.G (Grade 5 ): Geometry

CCSS.Math.Cont.5.G.B (Grade 5 ): Classify twodimensional figures into categories based on their properties.

CCSS.Math.Cont.5.G.B (Grade 5 ): Classify twodimensional figures into categories based on their properties.

CCSS.Math.Cont.5.G (Grade 5 ): Geometry

CCSS.Math.Cont.5.G.B (Grade 5 ): Classify twodimensional figures into categories based on their properties.

CCSS.Math.Cont.5.G.B (Grade 5 ): Classify twodimensional figures into categories based on their properties.

CCSS.Math.Cont.8.G (Grade 8 ): Geometry

CCSS.Math.Cont.8.G.A (Grade 8 ): Understand congruence and similarity using physical models, transparencies, or geometry software.

CCSS.Math.Cont.8.G.A.1 (Grade 8 ): Verify experimentally the properties of rotations, reflections, and translations:

CCSS.Math.Cont.8.G.A.1 (Grade 8 ): Verify experimentally the properties of rotations, reflections, and translations:

CCSS.Math.Cont.8.G.A (Grade 8 ): Understand congruence and similarity using physical models, transparencies, or geometry software.

CCSS.Math.Cont.8.G (Grade 8 ): Geometry

CCSS.Math.Cont.8.G.A (Grade 8 ): Understand congruence and similarity using physical models, transparencies, or geometry software.

CCSS.Math.Cont.8.G.A.1 (Grade 8 ): Verify experimentally the properties of rotations, reflections, and translations:

CCSS.Math.Cont.8.G.A.1 (Grade 8 ): Verify experimentally the properties of rotations, reflections, and translations:

CCSS.Math.Cont.8.G.A (Grade 8 ): Understand congruence and similarity using physical models, transparencies, or geometry software.

CCSS.Math.Cont.8.G (Grade 8 ): Geometry

CCSS.Math.Cont.8.G.A (Grade 8 ): Understand congruence and similarity using physical models, transparencies, or geometry software.

CCSS.Math.Cont.8.G.A (Grade 8 ): Understand congruence and similarity using physical models, transparencies, or geometry software.

CCSS.Math.Cont.8.G (Grade 8 ): Geometry

CCSS.Math.Cont.8.G.B (Grade 8 ): Understand and apply the Pythagorean Theorem.

CCSS.Math.Cont.8.G.B (Grade 8 ): Understand and apply the Pythagorean Theorem.