G9 Parallel and Perpendicular Lines

parallel lines

lines in the same plane that never intersect

perpendicular lines

Lines that intersect to form right angles

Transversal

a line that intersects two or more lines

alternate interior angles

angles inside the parallel lines on opposite sides of the transversal; congruent

alternate exterior angles

Angles outside the parallel lines and on opposite sides of the transversal; congruent

corresponding angles

angles in matching positions when a transversal crosses at least two lines

consecutive interior angles

angles between two lines on the same side of the transversal; supplementary

consecutive exterior angles

angles outside of the parallel lines on the same side of the transversal; supplementary

linear pair

two adjacent angles whose noncommon sides are opposite rays; supplementary

skew lines

two lines in three-dimensional space that are neither parallel nor intersecting

slope intercept form

y=mx+b

point-slope form

𝑦−𝑦=𝑚(𝑥−𝑥)

to find distance between line and a point not on the line

1. use the point and put in point slope form, to make perpendicular line (make slope the negative reciprocal), simplify to slope intercept form.

2. Make that new equation equal to the equation of the line to find x and y

3. use the new coordinates of x and y and the given point that isn’t on the line to use distance formula to find the distance.

to find distance between 2 parallel lines

1. use point slope form to find the perpendicular line and substitute the y intercept point from one of the lines, simplify to slope intercept form

2. make this perpendicular line equal to other parallel line to find x and y in slope intercept form

3. use that point and y intercept from the line that you chose in step 1 in distance formula to find distance.

proving parallel lines

• a pair of corresponding angles is congruent,

• a pair of alternate exterior angles is congruent,

• a pair of alternate interior angles is congruent,

• a pair of consecutive interior angles is supplementary

- a pair of consecutive exterior angles is congruent

•if two lines are perpendicular to the same line