Question

(17 PTS) GEOMETRY QUESTIONS, PLEASE HELP!

Answer 1

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.

Answer 2

14. 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.