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Chapter 3 Study Guide:
Important New Vocabulary:
Parallel Lines
Transversals
Alternate Exterior Angles
Pd.
TEST DATE: 11/23/10
Skew Lines
Corresponding Angles
Consecutive Interior
Angles
Parallel Planes
Alternate Interior Angles
Consecutive Exterior
Angles
Key Concepts & Skills:
 Identify angle relationships (e.g. corresponding) when two lines (not parallel) are
intersected by a transversal (3.1)
 Identify parallel, perpendicular and skew lines and parallel planes given in a diagram
 Complete a flow proof by adding reasons for each statement (3-2)
 Perpendicular Line Theorems (3-2)
o If 2 lines intersect to form a linear pair of congruent angles, then the lines are
perpendicular.
o If two sides of two adjacent acute angles are perpendicular, then the angles are
complementary.
o If two lines are perpendicular, then they intersect to form four right angles.
 Apply the parallel line theorems (e.g. Alternate Exterior Angle Theorem) to find angle
measures (3-3)
 Apply the converses of the parallel line theorems to prove lines are parallel (3-4)
 Apply the Dual Parallel and Dual Perpendicular Theorems to prove lines are parallel. (3-5)
 Find the distance between a point and a line and the distance between two parallel lines.
(3-5)
 Find the slope of lines (3-6 & 3-7)
 Determine whether liens are parallel, perpendicular or neither by analyzing the slopes of
the lines. (3-6 & 3-7)
 Write the equation of a line given various scenarios. (3-6 & 3-7)
Online Resources:
Review Problems:
I. Intersecting Lines and Planes:
II.
1)
Name all the planes that intersect plane OPT.
2)
suur
Name all segments that are parallel to NU .
3)
suur
Name all segments that intersect MP .
4)
suuur
Name all segments parallel to QX .
5)
Name all planes that intersect plane MHE.
6)
suur
Name all segments skew to AG
Find the values of x and y. Explain your reasoning.
Find x, y and z. Explain your reasoning.
7)
Find the values of angles 1, 2, 3, and 4. Explain your reasoning.
8)
9)
Find the value of x. Explain.
10)
Find the value of y. Explain.
III. Identify each pair of angles as corresponding,
alternate exterior, alternate interior, consecutive
interior, consecutive exterior, linear pair, vertical or
none.
1)
1 and 7
2)
4 and 13
3)
 10 and 13
4)
9 and 11
5)
8 and 14
6)
6 and 14
7)
4 and 9
8)
12 and 16
IV. State the postulate and theorem you would use to prove that lines a and b are
parallel.
1)
3)
5)
2)
4)
Which lines are parallel? Explain your reasoning.
Part V: Proofs
8)
Prove the following.
Part VI:
1)
Determine whether the lines are perpendicular, parallel or neither. Justify your answer.
a)
x + 3y = -4
6x – 2y = 8
c)
Use the slope to determine if the following lines are parallel, perpendicular or neither.
2)
a)
Determine if the intersection of AB and CD forms a right angle. Explain your reasoning.
A (-7, 0), B(-2, -1), C(-3, 6), D(-4, -3)
b)
A(1, 2), B(-2, -6), C(-1, 5), D(5, 2)
3)
Write the following equations of lines.
a)
b)
y=½x+3
y=½x–3
The line contains (-2, -2) and is parallel to –x + 2y = 10.