How to find out if lines are parallel - Math

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.

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.

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

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.

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

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

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

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

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.

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

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

Write the given equation in slope-intercept form:

The given line has slope , so this is the slope of any line parallel to that line.

We can use the slope formula , testing each of our choices.

, which is undefined

The only point whose inclusion yields a line with slope is .

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 .

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.

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.

To answer this question, we must determine the slopes of both lines. If a line has as its intercepts and , its slope is

The first line has as its slope

The second line has as its slope

Two lines are parallel if and only if their slopes are equal; this is not the case.

They are perpendicular if and only if the product of their slopes is . The product of the slopes of the given lines is

,

so they are perpendicular.

Two lines are parallel if and only if they have the same slope. The slope of one of the lines is 0.333. The other line has slope , which is equal to ; this is not equal to 0.333. The two lines are not parallel.

Two lines are parallel if and only if they have the same slope. The slope of one of the lines is . The slope of the other is , so the lines have the same slope. The lines are parallel.

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).