Intermediate Geometry : Lines
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Example Questions
Example Question #8 : How To Find Out If Lines Are Perpendicular
Are the lines of the equations
and
parallel, perpendicular, or neither?
Perpendicular
Parallel
Neither
Neither
Write each equation in the slope-intercept form 
Subtract 
The line of this equation has slope 
Subtract 
Multiply both sides by
The line of this equation has slope 
Two lines are parallel if and only if they have the same slope; this is not the case. They are perpendicular if and only if the product of their slopes is 
The correct response is that the lines are neither parallel nor perpendicular.
Example Question #9 : How To Find Out If Lines Are Perpendicular
Are the lines of the equations
and
parallel, perpendicular, or neither?
Parallel
Perpendicular
Neither
Neither
Write each equation in the slope-intercept form
Subtract 
Multiply both sides by 
The slope is the 
Add 
Multiply both sides by 
The slope is the 
Two lines are parallel if and only if they have the same slope; this is not the case. They are perpendicular if and only if the product of their slopes is 
Example Question #1 : How To Find Out If Lines Are Perpendicular
The slopes of two lines on the coordinate plane are 
True or false: the lines are perpendicular.
True
False
True
Two lines on the coordinate plane are perpendicular if and only if the product of their slopes is 
so the lines are indeed perpendicular.
Example Question #11 : How To Find Out If Lines Are Perpendicular
Two lines intersect at the point 
True or false: The lines are perpendicular.
True
False
False
Two lines are perpendicular if and only if the product of their slopes is 
To find the slope of the first line, set 
To find the slope of the second line, set 
The product of the slopes is
As the product is not 
Example Question #171 : Lines
The slopes of two lines are 6 and 
True
False
False
Two lines on the coordinate plane are perpendicular if and only if the product of their slopes is
The product is not equal to
Example Question #1 : Parallel Lines
Which answer contains all the angles (other than itself) that are congruent to Angle 1?
Angles 2 and 5
Angles 4 and 5
Angles 8 and 6
Angles 4, 5, and 8
Angles 2 and 4
Angles 4, 5, and 8
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
Angles 2 and 3 are congruent based on which Theorem?
Alternate Exteriors Angles
Consecutie Internior Angles
Vertical Angles
Corresponding Angles
Alternate Interior Angles
Vertical Angles
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 #3 : Parallel Lines
If angles 2 and 6 are congruent, lines AB and CD are parallel based on which theorem?
Consecutive Interior Angles
Vertical Angles
Corresponding Angles
Alternate Exterior Angles
Alternate Interior Angles
Corresponding Angles
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
What is the sum of Angle 3 and Angle 5?
15 deg
45 deg
90 deg
360 deg
180 deg
180 deg
Because of the Consecutive Interior Angle theorem, the sum of Angles 3 and 5 would be 180 deg.
Example Question #5 : Parallel Lines
If lines AB and CD are parallel, angles 1 and 8 are congruent based on which theorem?
Alternate Interior Angles
Vertical Angles
Corresponding Angles
Alternate Exterior Angles
Consecutive Interior Angles
Alternate Exterior Angles
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.
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