Download Geometry Name Review 3.1-3.4 Date Hour Identify the transversal

Geometry
Review 3.1-3.4
Name
Date
Hour
Identify the transversal and classify each angle pair as alternate interior, sameside interior, corresponding or alternate exterior.
1. ‹ 5 and ‹ 2
2. < 6 and < 3
1
3
6
5
3. < 2 and < 4
4
n
2
4. < 1 and < 2
l
m
Fill in the blank with congruent or supplementary. Draw an example of each.
5. If two parallel lines are cut by a transversal, then alternate interior angles are
___________________.
6. If two parallel lines are cut by a transversal, then alternate exterior angles are
___________________.
7. If two parallel lines are cut by a transversal, then corresponding angles are
___________________.
8. If two parallel lines are cut by a transversal, then same-side interior angles are
___________________.
9. Find the measure of each angle if m < 1 = 105˚.
p
q
1 3
2 4
5 6
7 8
Find the value of the variable. State the postulate or theorem that is related to
the measures of the angles. Show all work!
(3x + 20)˚
11.
12.
125˚
x˚
(8x - 15)˚
13.
14.
(21x)˚
(21x + 14)˚
(18x + 10)˚
(13x + 24)˚
15.
(15x)˚
16.
(9x - 6)˚
(3x + 18)˚
(12x + 17)˚
17.
(38x - 14)˚
18
(13x + 24)˚
(17x + 8)˚
(26x + 22)˚
Name the postulate or theorem that proves p // q. If the lines are not parallel,
write “not parallel.”
19. m < 1 ≅ m < 8
20. m < 4 ≅ m < 5
p
21. m < 2 ≅ m < 3
1
22. m< 4 + m < 6 = 180˚
2
q
23. m < 3 ≅ m < 6
24. m < 1 ≅ m < 7
25. m < 2 ≅ m < 5
26. m < 3 ≅ m < 7
3
4
5 6
7 8
Prove that p // q by finding the value of the variable and each angle measure.
State the postulate or theorem that justifies your answer.
27. m < 8 = (5x + 36)˚; m < 4 = (11x + 12)˚
p
x = _____, m < 8 = _____, m < 4 = _____
Therefore, by the ____________________________,
p // q.
1 3
2 4
q
5 6
7 8
28. m < 2 = (12x + 6)˚; m < 5 = (21x + 9)˚
x = _____, m < 2 = _____, m < 5 = _____
Therefore, by the ____________________________, p // q.
29. m < 3 = 99˚; m < 7 = (13x + 8)˚
x = _____, m < 3 = _____, m < 7 = _____
Therefore, by the ____________________________, p // q.
30. The shortest distance from any point to a line is _____________________.
L
31. Name the shortest segment from K to LN.
32. Write and solve an inequality for x.
8
K
M
x-5
N
Solve for x and y in each diagram.
33.
(7x – 2y)˚
34.
(2x + y) ˚ (10x - 4y) ˚
(5x)˚
35.
36.
(8x +4y) ˚
(4x + 10y) ˚ (11x +5y) ˚
(10x) ˚
Solve the system of equations.
37. x + y = 12
x– y=2
38. 2x + 4y = -4
3x + 5y = -3
39. x = y – 3
5x + 3y = 1
40. 5x + 2y = -1
3x + 7y = 11
Constructions
Construct a line parallel to the given line and through the given point.
41.
X
m
42.
X
n
Construct a line perpendicular to the given line at the given point on the lines.
43.
Y
44.
k
Z
g