Chapter 3 Review
Formal Geometry
Name: _________________________
____
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Identify the relationship between each pair of angles.
1.
2.
3.
4.
∠5 and ∠3
A.
Alternate Interior Angles
B.
Corresponding Angles
C.
Alternate Exterior Angles
D.
Consecutive Angles
∠1 and ∠7
A.
Alternate Interior Angles
B.
Corresponding Angles
C.
Alternate Exterior Angles
D.
Consecutive Angles
∠3 and ∠6
A.
Alternate Interior Angles
B.
Corresponding Angles
C.
Alternate Exterior Angles
D.
Consecutive Angles
∠3 and ∠7
A.
Alternate Interior Angles
B.
Corresponding Angles
C.
Alternate Exterior Angles
D.
Consecutive Angles
Chapter 3 Review
5.
Formal Geometry
Name: _________________________
____
The diagram shows the layout of Elm, Plum and Oak streets. Find the value
of 𝑥.
A.
43°
B.
180°
C.
103°
D.
137°
b
6.
a
Which statement is true based on the figure?
A.
a∥b
B.
b∥c
C.
a∥c
D.
d∥e
c
110°
65°
60°
120°
d
e
⃡ and 𝑋𝑌
⃡ are parallel, perpendicular, or neither.
7.
Determine whether 𝐴𝐵
𝐴(4, 3), 𝐵(8, 0), 𝑋(−4, 2), 𝑌(2, 10).
A.
B.
C.
D.
8.
Parallel
Perpendicular
Neither
Not enough information
A line perpendicular to a line that contains 𝐴(−2, 8)𝑎𝑛𝑑 𝐵(5, 1) has a slope of:
A.
B.
C.
D.
−1
1
−3
3
Chapter 3 Review
Formal Geometry
Name: _________________________
____
9-10.
Given:
Prove:
𝑝‖𝑞
𝑚∠1 + m∠8 = 180
Statements
𝑝‖𝑞
∠1 and ∠4 are supplementary.
∠5 and ∠8 are supplementary.
𝑚∠1 + 𝑚∠4 = 180
𝑚∠5 + 𝑚∠8 = 180
∠4 and ∠5 are supplementary.
Reasons
Given
If 2 angles form a linear pair, then they
are supplementary.
If 2 angles are supplementary, then
they add up to 180 degrees.
9.
𝑚∠4 + 𝑚∠5 = 180
10.
𝑚∠1 + 𝑚∠8 = 180
If two angles are congruent and
supplementary to the same angle, then
they are supplementary to each other.
9.
10.
Choose one of the following to complete the proof.
A.
If two lines are parallel, then consecutive interior angles are
supplementary. Consecutive Interior Angles Theorem.
B.
If two consecutive interior angles are congruent, then the lines are
parallel. Consecutive Interior Angles Converse Theorem.
C.
If two lines are parallel, then alternate interior angles are congruent.
Alternate Interior Angles Theorem.
D.
If two alternate interior angles are congruent, then the angles are
parallel. Alternate Interior Angles Converse Theorem.
Choose one of the following to complete the proof.
A.
If two angles are congruent, then they add up to 180 degrees.
Definition of Congruence.
B.
If an angle is a right angle, then it measures 90 degrees. Definition of a
right angle.
C.
If two lines are parallel, then supplementary angles are created.
Definition of parallel lines.
D.
If two angles are supplementary, then they add up to 180 degrees.
Definition of Supplementary Angles.
Chapter 3 Review
11.
12.
13.
14.
Formal Geometry
Name: _________________________
____
−13
Which equation of the line passes through (
A.
−8𝑥 + 12𝑦 = 24
B.
12𝑥 + 𝑦 = 47
C.
12𝑥 + 16𝑦 = −47
D.
−12𝑥 + 16𝑦 = 37
4
1
3
, − 2) with a slope of − 4 ?
Which equation of the line passes through (5, 6) and is parallel to the graph of
8
the line 𝑦 = 3 𝑥 + 7 .
A.
𝑦 = 3𝑥 −
8
22
B.
8
40
𝑦 = 3𝑥 +
3
C. 𝑦 = − 8 𝑥 −
3
34
3
8
D. 𝑦 = 16𝑥 + 3
3
Which equation of the line passes through (19, − 8) and is perpendicular to
11
the graph of the line 𝑦 = 13 𝑥 + 17 .
11
A.
𝑦 = 159𝑥 + 13
B.
13
𝑦 = − 11 𝑥 +
159
11
13
C. 𝑦 = − 11 𝑥 +
1247
11
D. 𝑦 = −13𝑥 − 13
Which equation of the line passes through (4,7) and is perpendicular to the
graph of the line that passes through the points (2,3) and (−4,9) ?
A.
𝑦 = 𝑥 + 11
B.
𝑦 = 2𝑥 + 5
1
1
C. 𝑦 = 2 𝑥 − 5
D. 𝑦 = 𝑥 + 3
Chapter 3 Review
Formal Geometry
Name: _________________________
____
15-16.
Given the following information, determine which lines,
if any, are parallel. State the postulate or theorem that
justifies your answer.
15.
16.
17.
18.
∠2 ≅ ∠5
A.
𝑡‖𝑦; If AIA are ≅, then the lines are parallel.
B.
𝑡‖𝑦; If corresponding angles are ≅, then the lines are parallel.
C.
𝑤‖𝑥; If AIA are ≅, then the lines are parallel.
D.
𝑤‖𝑥; If corresponding angles are ≅, then the lines are parallel.
∠3 ≅ ∠7
A.
𝑡‖𝑦; If corresponding angles are ≅, then the lines are parallel.
B.
𝑤‖𝑥; If corresponding angles are ≅, then the lines are parallel.
C.
𝑡‖𝑦 and 𝑤‖𝑥 because the angles are corresponding across all lines.
D.
No lines can be assumed parallel with the given information.
What is the shortest distance between a point and a line?
A.
The right triangle that connects the point to the origin.
B.
The line perpendicular to the given line that passes through the given
point.
C.
The line with a slope of zero that intersects the line.
D.
The line parallel to the given line that passes through the given point.
1
Line k is represented by the equation 𝑦 = 3 𝑥 + 3 . Which equation would you
use to determine the distance between the line k and point (0,0) .
A.
𝑦 = −3𝑥 + 5
B.
𝑦 = 2𝑥
C.
𝑦 = −2𝑥 + 3
D.
𝑦 = −3𝑥
1
1
Chapter 3 Review
Formal Geometry
Name: _________________________
____
Free Response. Partial credit will be awarded. Please write your complete proof on
the bubble sheet. Anything on this page will not be scored.
19. Given:
Prove:
𝑚‖𝑛; 𝑙 𝑖𝑠 𝑎 𝑡𝑟𝑎𝑛𝑠𝑣𝑒𝑟𝑠𝑎𝑙
∠7 ≅ ∠5
∠8 ≅ ∠6
Statements
1.
2. ∠7 ≅ ∠2
∠8 ≅ ∠4
3. ∠2 ≅ ∠5
∠4 ≅ ∠6
4.
Reasons
1. Given
2.
3.
4.
20. Write a coordinate proof for the following:
Given:
𝐴(−2, 0), 𝐵(0, 1), 𝐶(0, −3), 𝐷(2, − 2)
Prove:
∠𝐵𝐶𝐷 ≅ ∠𝐴𝐵𝐶