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  1. 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.
Panoyin
  1. Supplementary
    15. Congruent

    16. \(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 2}{4 - 5} = \frac{5}{-1} = -5 \\\\y - y_1 = m(x - x_1) \\y - 2 = -5(x - 5) \\y - 2 = -5(x)+ 5(5) \\y - 2 = -5x + 25 \\y = -5x + 27\)

    17. \(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - 3}{-5 - 7} = \frac{0}{-12} = 0 \\\\y - y_1 = m(x - x_1) \\y - 3 = 0(x - 7) \\y - 3 = 0(x) - 0(7) \\y - 3 = 0x - 0 \\y = 0x + 3\)

    18. \(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - (-2)}{5 - (-4)} = \frac{1 + 2}{5 + 4} = \frac{3}{9} = \frac{1}{3} \\\\y - y_1 = m(x - x_1) \\y - (-2) = \frac{1}{3}(x - (-4)) \\y + 2 = \frac{1}{3}(x + 4) \\y + 2 = \frac{1}{3}(x) + \frac{1}{3}(4) \\y + 2 = \frac{1}{3}x + 1\frac{1}{3} \\y = \frac{1}{3}x - \frac{2}{3}\)

    19. Perpendicular
    20. Neither
    21. Perpendicular
    22. Parallel

    23. Given: Transversal r cuts lines
                     l and m: <2 = <1
          Prove: l || m

      Statements  | Reasons                       
    1. <2 ≡ <1      | 1. They are congruent.
    2. <1 ≡ <3      | 2. They are congruent.
    3. <2 ≡ <3      | 3. They are parallel.
    4. l || m           | 4. They are parallel.

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