Parallel Lines

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Geometry › Parallel Lines

Questions 1 - 10

Transverselines

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

Angles 4, 5, and 8

Angles 2 and 4

Angles 2 and 5

Angles 8 and 6

Angles 4 and 5

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).

Transverselines

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

Angles 4, 5, and 8

Angles 2 and 4

Angles 2 and 5

Angles 8 and 6

Angles 4 and 5

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).

Find a line parallel to the line with the equation:

$y=\frac{1}{19}x+14$

Explanation

For two lines to be parallel, they must have the same slope. For a line in , or slope intercept form, corresponds to the slope of the line.

For the given line, . A line that is parallel must also then have the same slope.

Only the following line has the same slope:

Transverselines

Angles 2 and 3 are congruent based on which Theorem?

Vertical Angles

Alternate Interior Angles

Corresponding Angles

Consecutie Internior Angles

Alternate Exteriors 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.

A line is parallel to the line of the equation

and passes through the point .

Give the equation of the line in standard form.

None of the other choices gives the correct response.

Explanation

Two parallel lines have the same slope. Therefore, it is necessary to find the slope of the line of the equation

Rewrite the equation in slope-intercept form . , the coefficient of , will be the slope of the line.

Add to both sides:

Multiply both sides by $\frac{1}{7}$ , distributing on the right:

$\frac{1}{7} \cdot 7y = \frac{1}{7} \cdot( -5x+32)$

$y = -\frac{5}{7}x+\frac{32}{7}$

The slope of this line is $-\frac{5}{7}$ . The slope of the first line will be the same. The slope-intercept form of the equation of this line will be

$y =-\frac{5}{7}x+b$ .

To find , set and and solve:

$8 =-\frac{5}{7} (-2)+b$

$8 = \frac{10}{7} +b$

$\frac{56}{7} = \frac{10}{7} +b$

Subtract $\frac{10}{7}$ from both sides:

$\frac{56}{7} - \frac{10}{7} = \frac{10}{7} +b - \frac{10}{7}$

$b = \frac{46}{7}$

The slope-intercept form of the equation is $y =-\frac{5}{7}x+ \frac{46}{7}$

To rewrite in standard form with integer coefficients:

Multiply both sides by 7:

$7 y =7\left (-\frac{5}{7}x+ \frac{46}{7} \right )$

$7 y =7\left (-\frac{5}{7}x \right ) +7\left ( \frac{46}{7} \right )$

Add to both sides:

the correct equation in standard form.

A line is parallel to the line of the equation

and passes through the point .

Give the equation of the line in standard form.

None of the other choices gives the correct response.

Explanation

Two parallel lines have the same slope. Therefore, it is necessary to find the slope of the line of the equation

Rewrite the equation in slope-intercept form . , the coefficient of , will be the slope of the line.

Add to both sides:

Multiply both sides by $\frac{1}{7}$ , distributing on the right:

$\frac{1}{7} \cdot 7y = \frac{1}{7} \cdot( -5x+32)$

$y = -\frac{5}{7}x+\frac{32}{7}$

The slope of this line is $-\frac{5}{7}$ . The slope of the first line will be the same. The slope-intercept form of the equation of this line will be

$y =-\frac{5}{7}x+b$ .

To find , set and and solve:

$8 =-\frac{5}{7} (-2)+b$

$8 = \frac{10}{7} +b$

$\frac{56}{7} = \frac{10}{7} +b$

Subtract $\frac{10}{7}$ from both sides:

$\frac{56}{7} - \frac{10}{7} = \frac{10}{7} +b - \frac{10}{7}$

$b = \frac{46}{7}$

The slope-intercept form of the equation is $y =-\frac{5}{7}x+ \frac{46}{7}$

To rewrite in standard form with integer coefficients:

Multiply both sides by 7:

$7 y =7\left (-\frac{5}{7}x+ \frac{46}{7} \right )$

$7 y =7\left (-\frac{5}{7}x \right ) +7\left ( \frac{46}{7} \right )$

Add to both sides:

the correct equation in standard form.

Find a line parallel to the line with the equation:

$y=\frac{1}{19}x+14$

Explanation

For two lines to be parallel, they must have the same slope. For a line in , or slope intercept form, corresponds to the slope of the line.

For the given line, . A line that is parallel must also then have the same slope.

Only the following line has the same slope:

Transverselines

Angles 2 and 3 are congruent based on which Theorem?

Vertical Angles

Alternate Interior Angles

Corresponding Angles

Consecutie Internior Angles

Alternate Exteriors 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.

Suppose a line . What is the equation of a parallel line that intersects point ?

Explanation

A line parallel to must have a slope of two. Given the point and the slope, use the slope-intercept formula to determine the -intercept by plugging in the values of the point and solving for :

Plug the slope and the -intercept into the slope-intercept formula:

One line on the coordinate plane has its intercepts at and . A second line has its intercepts at and . Are the lines parallel, perpendicular, or neither?