Pairs of Lines and Angles
Lines that will not intersect and are coplanar
Parallel lines
If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.
Corresponding Angles Theorem
If two lines are cut by a transversal so that the alternate interior angles are congruent, then the lines are parallel.
Alternate Interior Angles Converse
y=3x, (-1,7)
about 3.2 units
y=2x+7, y=2x-2
about 4 units
Lines that will not intersect and are not coplanar
Skew lines
If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.
Alternate Interior Angles Theorem
If two lines are cut by a transversal so that the alternate exterior angles are congruent, then the lines are parallel.
Alternate Exterior Angles Converse
y=-4x, (6,-2)
About 5.3 units
y=-3x+1, y=-3x+4
about 0.9 units
Two angles that lie outside the lines and on opposite sides of the transversal
Alternate exterior angles
If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent.
Alternate Exterior Angles Theorem
If two lines are cut by a transversal so that the consecutive interior angles are supplementary, then the lines are parallel.
y=x-6, (-9,-3)
about 8.5 units
y=-4x+5, y=-4x+7
about 0.5 units
Two angles that lie between the two lines and on opposite sides of a transversal
Alternate interior angles
If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary.
Consecutive Interior Angles Theorem
If two lines are cut by a transversal so that the corresponding angles are congruent, then the lines are parallel.
Corresponding Angles Converse
y=-2x+1, (-4,4)
about 2.2 units
y=3x+6, y=3x-2
about 2.5 units
Two angles that lie between the two lines and on the same side of the transversal
What is the measure of angle 5 if angle 2 and angle 5 are consecutive interior angles and angle 2 measures 57 degrees?
123 degrees
If angle 3 equals 55 degrees and angle 5 equals 55 degrees and they are consecutive interior angles, are the two lines parallel?
NO!
Line which the slope is -3 and passes through (2,-4), (-1,4)
about 0.3 units
y=(-5/6)x-1, parallel line that passes through (6,-4)
about 1.5 units