Intermediate Geometry : How to find out if lines are parallel

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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Example Question #1 : Parallel Lines

Transverselines

Which answer contains all the angles (other than itself) that are congruent to Angle 1?

Possible Answers:

Angles 2 and 5

Angles 4, 5, and 8

Angles 2 and 4

Angles 8 and 6

Angles 4 and 5

Correct answer:

Angles 4, 5, and 8

Explanation:

Because of the Corresponding Angles Theorem (Angle 2 and Angle 5), Alternate Exterior Angles (Angle 2 and Angle 8), and Vertical Angles (Angle 2 and Angle 4). 

Example Question #2 : Parallel Lines

Transverselines

Angles 2 and 3 are congruent based on which Theorem?

Possible Answers:

Vertical Angles

Consecutie Internior Angles

Alternate Interior Angles

Alternate Exteriors Angles

Corresponding Angles

Correct answer:

Vertical Angles

Explanation:

Veritcal angles means that the angles share the same vertex. Angles 2 and 3 are a vertical pair of angles, which mean that they are congruent. 

Example Question #1 : How To Find Out If Lines Are Parallel

Transverselines

If angles  2 and 6 are congruent, lines AB and CD are parallel based on which theorem? 

Possible Answers:

Consecutive Interior Angles

Vertical Angles 

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Correct answer:

Corresponding Angles

Explanation:

Angles 2 and 6 are Corresponding Angles. If each of the set of angles were taken separately, angels 2 and 6 would occupy the same place and are thus corresponding angles. 

Example Question #4 : Parallel Lines

Transverselines

What is the sum of Angle 3 and Angle 5?

Possible Answers:

15 deg

360 deg

90 deg

45 deg

180 deg

Correct answer:

180 deg

Explanation:

Because of the Consecutive Interior Angle theorem, the sum of Angles 3 and 5 would be 180 deg. 

Example Question #5 : Parallel Lines

Transverselines

If lines AB and CD are parallel, angles 1 and 8 are congruent based on which theorem?

Possible Answers:

Vertical Angles

Alternate Interior Angles

Consecutive Interior Angles

Alternate Exterior Angles

Corresponding Angles

Correct answer:

Alternate Exterior Angles

Explanation:

Angles 1 and 8 are on the exterior of the parallel lines and are on opposite sides of the transversal. This means the Theorem is the Alternate Exterior Angle theorem. 

Example Question #2 : How To Find Out If Lines Are Parallel

Transverselines

If Angles 2 and 7 are congruent, line AB and CD are __________.

Possible Answers:

parallel

askance

skew

perpendicular

Correct answer:

parallel

Explanation:

Lines AB and CD are parallel based on the Alternate Exterior Angle theorem. 

Example Question #7 : Parallel Lines

Transverselines

If lines AB and CD are parallel, angles 5 and 1 are __________.

Possible Answers:

exterior angles

corresponding angles

alternate exterior angles

interior angles

alternate interior angles

Correct answer:

corresponding angles

Explanation:

If the two lines are parallel, the transverse line makes it so that angles 2 and 7 are corresponding angles. 

Example Question #3 : How To Find Out If Lines Are Parallel

Transverselines

If lines AB and CD are parallel, the sum of Angle 6 plus Ange 4 equals __________. 

Possible Answers:

180 deg

90 deg 

15 deg

45 deg

0 deg

Correct answer:

180 deg

Explanation:

If lines AB and CD are parallel, the sum of Angles 4 and 6 is 180 deg based on the Consecutive Interior Angle Theorem.

Example Question #9 : Parallel Lines

Transverselinestilted

If lines AB and CD are parallel, angles 2 and 7 are congruent based on which theorem?

Possible Answers:

Alternate Interior Angles

Consecutive Angles

Corresponding Angles

Alternate Exterior Angles

There is not enough information to determine 

Correct answer:

Alternate Exterior Angles

Explanation:

Angles 2 and 7 are both on the exterior side of the transverse, this means they are Alternate Exterior Angles.

Example Question #10 : Parallel Lines

Transverselinestilted

If lines AB and CD are parallel, which angles are congruent to Angle 3?

Possible Answers:

Angles 2, 7, and 6

Angles 7 and 6

Angles 5, 8, and 1

Angles 1 and 5

There is not enought information to determine

Correct answer:

Angles 2, 7, and 6

Explanation:

Angle 2 is congruent based on the Vertical Angle Theorem. Angle 7 is congruent based on the Corresponding Angles Theorem. Angle 6 is congruent based on the Alternate Interior Angles theorem. 

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