14.
Angles 4 and 6 are supplementary, because they are on the same line. Supplementary angles add up to 180 degrees, and a line must be 180 degrees.
15.
Angles 1 and 8 are congruent, because they are alternate exterior angles
16.
m = y2 - y1 / x2 - x1
m = 7 - 2 / 4 - 5
m = 5 / -1
m = -5
17.
m = 3 - 3 / 7 - (-5)
m = 0 / 12
m = 0
18.
m = 1 - (-2) / 5 - (-4)
m = 3 / 9
m = 1/3
19.
A = (0, 3) - B = (3,0)
m = 0 - 3 / 3 - 0
m = -3 / 3
m = -1
C = (0, -2) - D = (4, 2)
m = 2 - (-2) / 4 - 0
m = 4 / 4
m = 1
Perpendicular, because the slopes are opposite reciprocals.
20.
E = (1, 2) - F = (0, 0)
m = 0 - 2 / 0 - 1
m = -2 / -1
m = 2
G = (1, -3) - H = (3, 0)
m = 0 - (-3) / 3 - 1
m = 3 / 2
Neither, because the slopes are different.
21.
I = (0, 1) - J = (2, -4)
m = -4 - 1 / 2 - 0
m = -5/2
K = (-1, -2) - L = (4, 0)
m = 0 - (-2) / 4 - (-1)
m = 2/5
Perpendicular, because the slopes are opposite reciprocals.
22.
M = (-2, 2) - N = (2, 2)
Horizontal line
m = 0
O = (3, 0) - P = (-3, 0)
Horizontal line
m = 0
Parallel, because the slopes are the same.
23.
Angle 2 is congruent to angle 1 because of the alternate exterior angle theorem.
Angle 1 is congruent to angle 3 because of the vertical angle theorem.
Angle 2 is congruent to angle 3 because of substitution.
Line l is parallel to line m because the corresponding angles are congruent.
