Intermediate Geometry : Lines

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #6 : Parallel Lines

Transverselines

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

Possible Answers:

askance

parallel

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

alternate exterior angles

alternate interior angles

interior angles

corresponding 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 #8 : Parallel Lines

Transverselines

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

Possible Answers:

90 deg 

45 deg

15 deg

180 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:

Corresponding Angles

Alternate Exterior Angles

Consecutive Angles

There is not enough information to determine 

Alternate Interior Angles

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

There is not enought information to determine

Angles 7 and 6

Angles 1 and 5

Angles 5, 8, and 1

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. 

Example Question #181 : Lines

Where do the lines  and  intersect.

Possible Answers:

They never intersect.

Correct answer:

They never intersect.

Explanation:

By solving both equations to standard form , you can see that both lines have the same slope, and therefore will never intersect. 

Example Question #12 : How To Find Out If Lines Are Parallel

A line passes through both the coordinates  and . A line passing through which other pair of coodinates would be parallel to this line?

Possible Answers:

 and 

 and 

 and 

 and 

 and 

Correct answer:

 and 

Explanation:

The line has a slope of , so you must find a pair of points which has the same slope.

Example Question #12 : How To Find Out If Lines Are Parallel

Choose the equation that represents a line that is parallel to .

Possible Answers:

Correct answer:

Explanation:

Two lines are parallel if and only if they have the same slope. To find the slopes, we must put the equations into slope-intercept form,  , where  equals the slope of the line. In this case, we are looking for . To put into slope-intercept form, we must subtract  from each side of the equation, giving us . We then subtract  from each side, giving us . Finally, we divide both sides by , giving us , which is parallel to .

Example Question #184 : Coordinate Geometry

Which of the following lines are parallel?

Possible Answers:

None of these.

Correct answer:

None of these.

Explanation:

None of these lines are parallel.

In order for lines to be parallel, the lines must NEVER cross. Lines with identical slopes never cross. An example of two parallel lines would be:

Note that only the slope determines if line are parallel. 

Example Question #187 : Lines

Are the lines of the equations 

and

parallel, perpendicular, or neither? 

Possible Answers:

Neither

Perpendicular 

Parallel 

Correct answer:

Parallel 

Explanation:

Write each equation in the slope-intercept form  by solving for ; the -coefficient  is the slope of the line.

The first equation, 

,

is in the slope-intercept form  form. The slope is the -coefficient  .

 

 is not in this form, so it should be rewritten as such by multiplying both sides by :

The slope of the line of this equation is the -coefficient  

The lines of both equations have the same slope, , so it follows that they are parallel.

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