Common Core: High School - Geometry : Prove Geometric Theorems: Lines and Angles

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Example Question #11 : Prove Geometric Theorems: Lines And Angles

Prove that if , then lines  and  are parallel.

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Possible Answers:

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Correct answer:

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Explanation:

Follow the detailed proof below.

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Example Question #21 : Prove Geometric Theorems: Lines And Angles

Are lines  and  parallel?

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Possible Answers:

No

Yes

Correct answer:

No

Explanation:

 The angles formed by the transversal line intersecting lines  and  does not form congruent opposite vertical angles.  Therefore these two lines are not congruent.

Example Question #603 : High School: Geometry

What are the values of angles  and ?

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Possible Answers:

Correct answer:

Explanation:

We are able to use the relationship of opposite vertical angles to solve this problem.  The given angle and angle  are opposite vertical angles and therefore must be congruent.  So  is supplementary to both angles  and  so they must be congruent.   and  are also opposite vertical angles so they must be congruent in that respect as well.  So

 

Example Question #12 : Prove Geometric Theorems: Lines And Angles

Which of the following describes  and ?

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Possible Answers:

These angles are complementary angles, therefore they sum to 90

These angles are corresponding angles, therefore they are equal

These angles are alternate interior angles, therefore they are equal

These angles are alternate exterior angles, therefore they are equal

Correct answer:

These angles are alternate exterior angles, therefore they are equal

Explanation:

To answer this question, we must understand the definition of alternate exterior angles.  When a transversal line intersects two parallel lines, 4 exterior angles are formed.  Alternate exterior angles are angles on the outsides of these two parallel lines and opposite of each other.

Example Question #605 : High School: Geometry

True or False: The following figure shows a line segment.

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Possible Answers:

True

False

Correct answer:

False

Explanation:

The figure shows a ray.  A ray has a single endpoint and the other end extends infinitely.  This is represented by an arrowhead on the end that extends infinitely.

Example Question #606 : High School: Geometry

Solve for ?

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Possible Answers:

Correct answer:

Explanation:

 and the given angle are supplementary angles.  This means that they sum up to 180 degrees.

So

Example Question #236 : Congruence

Prove that if lines  and  are parallel, then the same side interior angles,  and , are congruent.

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Possible Answers:

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Correct answer:

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Explanation:

Follow the detailed proof below.

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Example Question #607 : High School: Geometry

Prove that if the following lines  and  are parallel, then the interior angles on the same side of the transversal are supplementary.

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Possible Answers:

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Correct answer:

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Explanation:

Follow the detailed proof below.

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Example Question #608 : High School: Geometry

Prove that angles 1 and 2 are complementary.

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Possible Answers:

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Correct answer:

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Explanation:

Follow the detailed proof below.

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Example Question #21 : Prove Geometric Theorems: Lines And Angles

Prove that if the following lines  and  are parallel, then their alternate interior angles are equal.

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Possible Answers:

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Correct answer:

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Explanation:

Follow the detailed proof below.

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All Common Core: High School - Geometry Resources

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