Download Name: Period: ______ Geometry Unit 3: Parallel and Perpendicular

Name: _______________________________________________ Period: _________
Unit 3: Parallel and Perpendicular Lines
Geometry
Homework
Section 3.1: Properties of Parallel Lines
PART 1
Classify each pair of angles as alternate interior angles, alternate exterior angles, or corresponding
angles.
1.
2.
3.
4.
5.
Find m∠1 and then m∠2. Justify each answer.
6.
7.
8.
9.
Identify all the numbered angles that are congruent to the given angle.
10.
11.
12.
Find the value of the variables.
13.
14.
REVIEW: Answer always, sometimes, or never for each question.
1.  Two distinct points determine a line.
2.  Supplementary angles are adjacent.
3.  Coplanar points are collinear.
4.  Adjacent angles are congruent.
5.  Parallel lines are coplanar.
6.  Two intersecting lines are coplanar.
7.  An equiangular triangle is equilateral.
15.
Section 3.1: Properties of Parallel Lines
PART 2
Classify each pair of angles as same-side interior, same-side exterior, or a linear pair.
1.
2.
3.
4.
5.
Find the value of the variable.
6.
7.
8.
Find the m∠1 and then m∠2. Justify each answer.
10.
11.
Find the measures of all the numbered angles.
13.
14.
REVIEW: Answer always, sometimes, or never for each question.
1.  A scalene triangle is regular.
2.  A theorem is a proven conjecture.
3.  Planes intersect in a point.
4.  Space is an infinite number of points.
5.  A line can be named using three points.
6.  Two points are collinear.
7.  Two lines which never intersect are parallel.
8.  If two lines intersect, their intersection is a point.
9.
12.
Section 3.2: Proving Lines Parallel
Which lines or segments are parallel? Justify your answer with a theorem or postulate.
1.
2.
3.
4.
5.
6.
Determine the value of x that makes r ∥ s. Then find the measure of each labeled angle.
7.
8.
9.
10.
11.
12.
Use the given information to determine which lines, if any, are parallel.
Justify each conclusion with a theorem or postulate.
13. ∠11 is supplementary to ∠10
14. ∠6 ≅ ∠9
15. ∠13 ≅ ∠ 15
16. ∠13 is supplementary to ∠14
17. ∠12 is supplementary to ∠3
18. ∠2 ≅ ∠13
REVIEW: Find the value of all of the angles.
1.
2.
3.
Find the value of each variable.
1.
2.
5.
Section 3.3: Parallel and Perpendicular Lines
3.
6.
7.
Find the measure of each numbered angle.
9.
10.
12.
4.
13.
8.
11.
14.
REVIEW: Use the diagram to name each of the following. Assume that lines and planes that appear to be
parallel are parallel.
1. 
A pair of parallel planes
2.  All lines that are parallel to AB
3.  All lines that are parallel to DH
4.  Two lines that are skew to EJ
5.  All lines that are parallel to plane JFAE
6.  A plane parallel to LH
Section 3.4: The Coordinate Plane
Graph each point on the same coordinate plane.
1. A(-2, 5)
2. B(5, -2)
3. C(0, 6)
4. D(-4, 0)
5. E(-4,-2)
6. F(4, 3)
Find the distance between the points.
7. L(-4, 11), M(-3, 4)
8. N(1, 0), P(3, 8)
10. S(0, 5), T(0, -3)
11. U(11, 0), V(-1, 0)
9. Q(10, 10), R(10, -2)
12. W(2, 7), X(1, 2)
Find the coordinates of the midpoint of each segment.
13. A(6, 7), B(4, 3)
14. C(-1, 5), D(2, -3)
16. O(0, 0), G(-5, 12)
17. H(2.8, 1.1), I(3.4, 5.7)
15. E(14,-2), F(7,-8)
18. J(2 ½ , - ¼ ) and K (3 ¼ , -1)
19. The midpoint of AB is (1, 2).The coordinates of A are (-3, 6). Find the coordinates of B.
20. The midpoint of CD is (4, 11).The coordinates of D are (4, 12). Find the coordinates of C.
21. The midpoint of EF is (-3, 7).The coordinates of E are (-3, 10). Find the coordinates of F.
REVIEW: Write a conditional, converse, inverse, contrapositive, and biconditional for each statement.
1.  Triangle’s angles have a sum of 180°.
2.  Transversals intersect two lines.
3.5: Lines in the Coordinate Plane
Graph each line on a different coordinate plane.
1. y = 5x + 4
2. x = -2
3. 3x + 9y = 18
4. y = -2x
6. y = -x
7. y = 1/2x – 3
8. y = 6
9. y = -2/3x + 4
5. y = x
10. 2x – 3y = 6
Write an equation of a line in slope intercept form given the following information.
11. m = 1/3, (3, -6)
12. m = -2, (5, 2)
13. (2, 7) and (3, 4)
14. (-1, 3) and (0, 4)
15. Parallel to 6x – 10y = 5 and through (-5, 3)
16. Parallel to y = -1 and through (5, 7)
17. Perpendicular to 3x + 2y = -6 and through (3, 2) 18. Perpendicular to y=3/4x + 22 and through (12, 8)
REVIEW: Name the intersection of each.
1. 
Plane JCD and AF
2.  FG and HD
3.  AJ and JC
4.  Plane JCD and plane BGH
5.  Plane ALH and plane FGD
6.  Plane FGA, plane JCD, and plane BHD
Unit 3 Review
For questions 1 – 3, suppose a ║ b and c ║ d.
1. ∠2 and ∠10 are what kind of angles?
2. ∠3 and what angle are alternate interior angles?
3. ∠9 and ∠8 are what kind of angles?
4. Which angle could you show is congruent to ∠11 to prove a ║ b?
5. What relationship between ∠6 and ∠11 shows c ║ d?
For questions 6 – 11, suppose a ║ b and c ║ d.
6. If m∠6 = 59, then find m∠11.
7. If m∠2 = 70, then find m∠6.
9. If m∠7 = 110, then find m∠10.
10. If m∠4 = 45, then find m∠12.
Identify all pairs of each type of angle in the diagram.
12. Corresponding angles
13. Alternate interior angles
14. Alternate exterior angles
15. Same-side interior angles
16. Same-side exterior angles
17. Linear pairs
18. Vertical angles
Find the value of the variables.
19.
20.
21.
22.
23.
24.
8. If m∠1 = 130, then find m∠5.
11. If m∠8 = 67, then find m∠6.
25.
Write an equation of a line with the following criteria.
26. Parallel to y = x – 1 through (1, 2)
27. Parallel to y = -1/2x + 2 through (-5, 7)
28. Perpendicular to y = 1/2x + 1 through (-2, 1)
29. Perpendicular to y = -3x + 2 through (3, 0)
30. Through points (2, 1) and (-1, -8)
31. Through points (-4, 2) and (8, 6)
Graph.
32. y = 2x – 1 33. y = -3x + 4
34. y = -2/3x
35. y = 4/3x – 4
36. x = -4
37. y = 5
Choose the correct vocabulary term to complete each sentence.
38. In a triangle, an angle is right, obtuse, or ______________.
39. A(n) ______________angle has a measure between 90 and 180.
40. When two coplanar lines are cut by a transversal, two angles that are in similar positions on the same side of the
transversal are called ______________.
41. The measure of a(n) ______________ angle of a triangle is equal to the sum of the measure of its two remote interior
angles.
42. The linear equation y – 3 = 4(x + 5) is written in ______________ form.
43. From the ______________ form of a linear equation, you can easily red the value of the slope and the value of the
y-intercept.
44. When two coplanar lines are cut by a transversal, the angles between the two lines and on opposite sides of the
transversal are called ______________.