Common Core: 8th Grade Math : Use Informal Arguments to Establish Facts about the Angle Sum and Exterior Angle of Triangles: CCSS.Math.Content.8.G.A.5

Example Questions

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Example Question #11 : Use Informal Arguments To Establish Facts About The Angle Sum And Exterior Angle Of Triangles: Ccss.Math.Content.8.G.A.5

The image provided contains a set of parallel lines,  and , and a transversal line, . Which angle is NOT equal to angle

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other.

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

• Vertical angles are congruent
• Corresponding angles are congruent
• Alternate interior angles are congruent
• Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships.

Angle  and  are vertical angles.

Angle  and  are corresponding angles.

Angle  and  are exterior angles.

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and

For this problem, we want to find the angle that is not equal to to angle . Let's look at our answer choices:

Angle  and  are vertical angles, which means they are congruent.

Angle  and   are alternate interior angles, which means they are congruent.

Angle  and  are corresponding angles, which means they are congruent.

However, angle  and  do not share a common angle relationship; thus they are not congruent.

Example Question #82 : Geometry

The image provided contains a set of parallel lines,  and , and a transversal line, . Which angle is NOT equal to angle

Explanation:

First, we need to define some key terms:

Parallel Lines: Parallel lines are lines that will never intersect with each other.

Transversal Line: A transversal line is a line that crosses two parallel lines.

In the the image provided, lines  and  are parallel lines and line  is a transversal line because it crosses the two parallel lines.

It is important to know that transversal lines create angle relationships:

• Vertical angles are congruent
• Corresponding angles are congruent
• Alternate interior angles are congruent
• Alternate exterior angles are congruent

Let's look at angle  in the image provided below to demonstrate our relationships.

Angle  and  are vertical angles.

Angle  and  are corresponding angles.

Angle  and  are exterior angles.

Angle  is an exterior angle; therefore, it does not have an alternate interior angle. In this image, the alternate interior angles are the angle pairs  and  as well as angle  and

For this problem, we want to find the angle that is not equal to to angle . Let's look at our answer choices:

Angle  and  are vertical angles, which means they are congruent.

Angle  and   are alternate exterior angles, which means they are congruent.

Angle  and  are corresponding angles, which means they are congruent.

However, angle  and  do not share a common angle relationship; thus they are not congruent.

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