Download Geometry Semester 1 Final Semester 1 Practice Final

First Semester Practice Final Geometry
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Refer to Figure 1.
m
n
B
A
H
D
C
K
J
G
F p
Figure 1
1. Name the plane containing lines m and p.
a. n
b. GFC
c. H
d. JDB
2. What is another name for line n?
a. line JB
c.
b.
d. AC
3. Name three points that are collinear.
H
B
A
D
J
G
C
F
a. B, G, F
b. C, D, H
Refer to Figure 2.
c. J, G, F
d. J, D, G
B
L
A
D
K
C
F
G
Figure 2
4. How many planes are shown in the figure?
a. 4
b. 3
c. 5
d. 6
5. How many planes contain points B, C, and A?
a. 1
c. 0
b. 2
d. 3
Find the measurement of the segment.
6.
mm,
P
mm
R
PS = ?
a. 32.7 mm
b. 5.1 mm
S
c. 32.5 mm
d. 32.4 mm
7. Find the value of the variable and LN if M is between L and N.
a. a = 3.73, LN = 29.87
b. a = 7, LN = 105
c. a = 8, LN = 120
d. a = 7, LN = 49
8. Find the value of the variable and GH if H is between G and I.
a. b = 1.2, GH = 6.8
b. b = 1.22, GH = 7.11
c. b = 3, GH = 9
d. b = 3, GH = 16
Use the Distance Formula to find the distance between each pair of points.
y
6
10.
5
4
3
2
1
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6 x
T (2, –2)
–2
–3
–4
W (–3, –5)
–5
–6
a.
b. 4
c.
d. 6
Find the coordinates of the midpoint of a segment having the given endpoints.
11.
a.
c.
b.
d.
a.
c.
b.
d.
12.
In the figure,
bisects
.
F
x
G
y
K
H
13. If
a. 33
b. 58
In the figure,
and
and
, find x.
c. 11
d. 29
are opposite rays.
and
bisects
.
J
P
1
K
2
3 4
N
M
L
14. If
a. 153
b. 33
and
15. If
a. 26.67
b. 13
, what is
and
, what is
?
c. 27
d. 12
?
c. 41
d. 15.67
Use the figure to find the angles.
I
H
G
J
2
1
M
Q
K
L
16. Name two acute vertical angles.
a.
b.
c.
d.
17. Name a pair of obtuse adjacent angles.
a.
b.
c.
d.
18. Name a linear pair.
a.
b.
c.
d.
19. Name an angle supplementary to
a.
b.
.
c.
d.
20. Name two obtuse vertical angles.
a.
b.
c.
d.
21. The measures of two complementary angles are
and
a. 42, 48
c. 8.75
b. 4.25
d. 96, 84
. Find the measures of the angles.
Make a conjecture about the next item in the sequence.
22.
a. 1024
b. 1025
c. 4096
d. 1022
Determine whether the conjecture is true or false. Give a counterexample for any false conjecture.
23. Given:
Conjecture:
a. False;
b. True
c. False;
d. False;
Refer to the figure below.
B
C
A
D
G
F
H
I
29. Name all segments parallel to
a.
b.
30. Name all planes intersecting plane
a.
b.
.
c.
d.
.
c.
d.
Determine the slope of the line that contains the given points.
31.
a.
5
2
b.

c.
2
5
d. 0
2
5
Determine whether
and
are parallel, perpendicular, or neither.
32.
a. parallel
b. perpendicular
c. neither
33.
a. perpendicular
b. parallel
c. neither
Write an equation in slope-intercept form of the line having the given slope and y-intercept.
34.
a.
c.
b.
d.
Write an equation in point-slope form of the line having the given slope that contains the given point.
35.
a.
b.
c.
d.
a.
b.
c.
d.
36.
Given the following information, determine which lines, if any, are parallel. State the postulate or theorem that
justifies your answer.
37.
c
10
d
9
2
1
4
a
3
5
b
a.
b.
c.
d.
11
6
8
7
; congruent corresponding angles
; congruent corresponding angles
; congruent alternate interior angles
; congruent alternate interior angles
38.
c
O
d
g
Q
H
N
L
f
K
a
J
M
P
b
a.
b.
c.
d.
; congruent corresponding angles
; congruent corresponding angles
; congruent alternate exterior angles
; congruent alternate exterior angles
Find each measure.
39.
2
59°
47°
1
3
64°
a.
b.
c.
d.
40.
45°
43°
2
39°
1
3
a.
b.
c.
d.
Name the congruent angles and sides for the pair of congruent triangles.
41.
a.
b.
c.
d.
Identify the congruent triangles in the figure.
42.
M
a.
b.
J
N
K
O
L
c.
d.
Short Answer
43. In the figure,
Find
1
2
44. Write an equation in slope-intercept form of the line joining the points
and
first semester practice final geometry
Answer Section
MULTIPLE CHOICE
1. ANS: B
A plane is a flat surface made up of points. A plane is named by a capital script letter or by the letters naming three
noncollinear points.
Feedback
A
B
C
D
Is that the way you name a plane?
Correct!
Is that the way you name a plane?
Do three collinear points name a plane?
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.1 Identify and model points, lines, and planes.
NAT: NCTM GM.2
STA: 1.3.1
TOP: Identify and model points, lines, and planes.
KEY: Points | Lines | Planes
2. ANS: B
A line is made up of points with an arrowhead at each end. A, D, and C are points on line n. A line is represented
by ‘line DC’ or
but not just DC.
Feedback
A
B
C
D
Are those points on line n?
Correct!
Are those points on line n?
Is that how a line is named?
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.1 Identify and model points, lines, and planes.
NAT: NCTM GM.2
STA: 1.3.1
TOP: Identify and model points, lines, and planes.
KEY: Points | Lines | Planes
3. ANS: A
Collinear points are points on the same line.
Feedback
A
B
C
D
Correct!
Are those points on the same line?
What does collinear mean?
Are those points on the same line?
PTS: 1
DIF: Average
REF: Lesson 1-1
NAT: NCTM GM.2
STA: 1.3.1
KEY: Collinear Points
4. ANS: C
Since the ends are triangles, there are three sides plus two ends.
OBJ: 1-1.2 Identify collinear points.
TOP: Identify collinear points.
Feedback
A
B
C
D
Did you count the back side?
Did you count the ends?
Correct!
Where is the sixth side?
PTS: 1
DIF: Basic
REF: Lesson 1-1
OBJ: 1-1.4 Identify intersecting lines and planes in space.
NAT: NCTM ME.1
STA: 1.3.1
TOP: Identify intersecting lines and planes in space.
KEY: Planes | Planes in Space
5. ANS: A
B, C, and A make up the back face of the prism.
Feedback
A
B
C
D
Correct!
Where is the second plane?
Do the points determine a face of the prism?
Where are the second and third planes?
PTS: 1
DIF: Average
REF: Lesson 1-1
OBJ: 1-1.4 Identify intersecting lines and planes in space.
NAT: NCTM ME.1
STA: 1.3.1
TOP: Identify intersecting lines and planes in space.
KEY: Planes | Planes in Space
6. ANS: C
PS has the same length as PR and RS combined.
Feedback
A
B
C
D
Did you add correctly?
PS contains both PR and RS.
Correct!
Try adding that again.
PTS: 1
DIF: Basic
REF: Lesson 1-2
OBJ: 1-2.1 Measure segments.
NAT: NCTM ME.2 | NCTM ME.2a
STA: 1.2.2
TOP: Measure segments.
KEY: Measurement | Line Segments
7. ANS: B
Solve for a first using the two values of LM.
. Solve for LN.
Feedback
A
B
C
D
Which two segments in the question are the same?
Correct!
Which two segments in the question are the same?
Which segment are you solving for?
PTS:
NAT:
KEY:
8. ANS:
1
DIF: Basic
NCTM NO.1
Measurement | Compute Measures
C
REF: Lesson 1-2
STA: 1.1.1
OBJ: 1-2.3 Compute with measures.
TOP: Compute with measures.
Solve for b first using the two values of HI.
. Solve for GH.
Feedback
A
B
C
D
Which two segments in the question are the same?
Which two segments in the question are the same?
Correct!
Which segment are you solving for?
PTS: 1
DIF: Average
REF: Lesson 1-2
NAT: NCTM NO.1
STA: 1.1.1
KEY: Measurement | Compute Measures
9. ANS: D
The distance between two points a and b is
or
.
OBJ: 1-2.3 Compute with measures.
TOP: Compute with measures.
Feedback
A
B
C
D
You are looking for the measure, not the midpoint.
You are looking for the measure, not the half measure.
Add those numbers again.
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
10. ANS:
1
DIF: Average
REF: Lesson 1-3
1-3.1 Find the distance between two points on a number line.
NCTM GM.2 | NCTM GM.2a
STA: 1.3.5
Find the distance between two points on a number line.
Distance | Number Lines | Distance Between Two Points
C
The Distance Formula is
.
Feedback
A
B
C
D
With distance you subtract the coordinates.
Did you use the distance formula correctly?
Correct!
Be a little more precise.
PTS:
OBJ:
NAT:
TOP:
KEY:
11. ANS:
1
DIF: Basic
REF: Lesson 1-3
1-3.2 Find the distance between two points on a coordinate plane.
NCTM GM.2 | NCTM GM.2a
STA: 1.3.5
Find the distance between two points on a coordinate plane.
Distance | Coordinate Plane | Distance Between Two Points
C
The formula for the midpoint between two points
Feedback
A
B
Did you use the Midpoint Formula?
Did you use the Midpoint Formula correctly?
is
.
C
D
Correct!
Do you subtract and then divide by two?
PTS:
NAT:
KEY:
12. ANS:
1
DIF: Average
NCTM ME.1
Midpoint | Line Segment
A
REF: Lesson 1-3
STA: 1.2.2
OBJ: 1-3.3 Find the midpoint of a segment.
TOP: Find the midpoint of a segment.
The formula for the midpoint between two points
is
.
Feedback
A
B
C
D
Correct!
You are finding the difference between the two points.
Do you add then divide by two or subtract?
You are finding the midpoint, not the distance.
PTS:
NAT:
KEY:
13. ANS:
1
DIF: Average
NCTM ME.1
Midpoint | Line Segment
D
Since
find x.
bisects
,
and
REF: Lesson 1-3
STA: 1.2.2
OBJ: 1-3.3 Find the midpoint of a segment.
TOP: Find the midpoint of a segment.
. Solve for v, then substitute into either side of the equation to
Feedback
A
B
C
D
Don’t forget to subtract.
You are not finding the measure of FGH. You are finding x.
You are not finding v. You are finding x.
Correct!
PTS:
NAT:
KEY:
14. ANS:
1
DIF: Basic
REF: Lesson 1-4
NCTM GM.1 | NCTM GM.1a
STA: 1.3.3
Angles | Congruent Angles | Congruency
C
Feedback
A
B
C
D
That is the measure of JKM.
You forgot to add in x.
Correct!
Opposite rays add up to 180.
PTS: 1
DIF: Average
REF: Lesson 1-4
OBJ: 1-4.3 Identify and use congruent angles.
TOP: Identify and use congruent angles.
OBJ:
STA:
KEY:
15. ANS:
1-4.4 Identify and use the bisector of an angle.
NAT: NCTM GM.1 | NCTM GM.1a
1.3.1 | 1.3.4 TOP: Identify and use the bisector of an angle.
Angle Bisectors
C
Feedback
A
B
C
D
Which angles form NKL?
Did you solve for s instead of the angle measure?
Correct!
These angles do not form a straight angle.
PTS: 1
DIF: Average
REF: Lesson 1-4
OBJ: 1-4.4 Identify and use the bisector of an angle.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 1.3.1 | 1.3.4 TOP: Identify and use the bisector of an angle.
KEY: Angle Bisectors
16. ANS: B
Vertical angles are two nonadjacent angles formed by two intersecting lines. Acute angles measure less than 90
degrees.
Feedback
A
B
C
D
You are looking for vertical angles, not adjacent angles.
Correct!
You are looking for vertical angles, not a linear pair.
What is the definition of acute?
PTS: 1
DIF: Basic
REF: Lesson 1-5
OBJ: 1-5.1 Identify and use special pairs of angles.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 1.3.1
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
17. ANS: B
Adjacent angles are two angles that lie in the same plane, have a common vertex, and a common side, but no
common interior points. Obtuse angles measure greater than 90 degrees.
Feedback
A
B
C
D
You are looking for adjacent angles, not vertical angles.
Correct!
You are looking for adjacent angles, not a linear pair.
What is the definition of obtuse?
PTS: 1
DIF: Basic
REF: Lesson 1-5
OBJ: 1-5.1 Identify and use special pairs of angles.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 1.3.1
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
18. ANS: C
A linear pair is a pair of adjacent angles whose noncommon sides are opposite rays.
Feedback
A
You are looking for a linear pair, not vertical angles.
B
C
D
You are looking for a linear pair, not just adjacent angles.
Correct!
You are looking for a linear pair which, by definition, must be adjacent.
PTS: 1
DIF: Average
REF: Lesson 1-5
OBJ: 1-5.1 Identify and use special pairs of angles.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 1.3.1
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
19. ANS: A
Supplementary angles are two angles whose measures have a sum of 180.
Feedback
A
B
C
D
Correct!
What is the definition of supplementary?
Do the measures have a sum of 180 degrees?
What is the definition of supplementary?
PTS: 1
DIF: Basic
REF: Lesson 1-5
OBJ: 1-5.1 Identify and use special pairs of angles.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 1.3.1
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
20. ANS: D
Vertical angles are two nonadjacent angles formed by two intersecting lines. Obtuse angles measure greater than
90 degrees.
Feedback
A
B
C
D
You are looking for vertical angles, not adjacent angles.
What is the definition of obtuse?
You are looking for vertical angles, not a linear pair.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 1-5
OBJ: 1-5.1 Identify and use special pairs of angles.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 1.3.1
TOP: Identify and use special pairs of angles.
KEY: Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
21. ANS: A
Complementary angles are two angles whose measures have a sum of 90.
Feedback
A
B
C
D
Correct!
Is that the value of q, or the measure of the angles?
What is the definition of complementary?
Is the sum of those angles 90?
PTS:
OBJ:
STA:
KEY:
22. ANS:
1
DIF: Average
REF: Lesson 1-5
1-5.1 Identify and use special pairs of angles.
NAT: NCTM GM.1 | NCTM GM.1a
1.3.1
TOP: Identify and use special pairs of angles.
Adjacent Angles | Vertical Angles | Linear Pair | Complementary Angles | Supplementary Angles
A
Start with 1. Add, subtract, or multiply the same number to each number to get the next one.
Feedback
A
B
C
D
Correct!
What operations are involved?
Didn’t you carry the conjecture too far?
Check your math.
PTS: 1
DIF: Basic
REF: Lesson 2-1
OBJ: 2-1.1 Make conjectures based on inductive reasoning.
NAT: NCTM RP.2
STA: 3.3.4
TOP: Make conjectures based on inductive reasoning.
KEY: Inductive Reasoning | Conjectures
23. ANS: D
Because m is squared in the example, m could be positive or negative.
Feedback
A
B
C
D
Subtract 6 from both sides.
What about negative numbers?
Subtract 6 from both sides.
Correct!
PTS: 1
DIF: Basic
REF: Lesson 2-1
OBJ: 2-1.2 Find counterexamples.
NAT: NCTM RP.3 STA: 3.3.4
TOP: Find counterexamples.
KEY: Counterexamples
24. ANS: A
Two or more statements can be joined to form a compound statement. A conjunction is a compound statement
formed by joining two or more statements with the word and.
Feedback
A
B
C
D
Correct!
What does statement r say?
Are four points always coplanar?
Does a decagon have 12 sides?
PTS: 1
DIF: Basic
REF: Lesson 2-2
OBJ: 2-2.1 Determine truth values of conjunctions and disjunctions.
NAT: NCTM RP.3 STA: 3.3.4
TOP: Determine truth values of conjunctions and disjunctions.
KEY: Truth Values | Conjunctions | Disjunctions
25. ANS: B
Two or more statements can be joined to form a compound statement. A disjunction is a compound statement
formed by joining two or more statements with the word or. The symbol for logical or is .
Feedback
A
B
C
D
What is the symbol for logical and?
Correct!
What does statement q say?
Which of those statements is false?
PTS: 1
DIF: Average
REF: Lesson 2-2
OBJ: 2-2.1 Determine truth values of conjunctions and disjunctions.
NAT: NCTM RP.3 STA: 3.3.4
TOP: Determine truth values of conjunctions and disjunctions.
KEY: Truth Values | Conjunctions | Disjunctions
26. ANS: A
The first statement column in a truth table contains half Ts, half Fs, grouped together. The second statement
column in a truth table contains the same, but they are grouped by half the number that the first column was. The
third statement column contains the same but they are grouped by half the number that the second column was.
Use the truth values of the first three columns to determine the truth values for the last two columns. The symbol
for not is . The symbol for logical and is .
Feedback
A
B
Correct!
Check the values for the last two columns carefully.
PTS: 1
DIF: Average
NAT: NCTM RP.3 STA: 3.3.4
KEY: Truth Tables
27. ANS: C
The converse of a conditional statement
is also known as
REF: Lesson 2-2
OBJ: 2-2.2 Construct truth tables.
TOP: Construct truth tables.
exchanges the hypothesis and conclusion of the conditional. It
.
Feedback
A
B
C
D
Check the statement again.
Check the statement again.
Correct!
What is the definition of converse?
PTS: 1
DIF: Basic
REF: Lesson 2-3
OBJ: 2-3.2 Write the converse of if-then statements.
NAT: NCTM RP.3
STA: 3.3.4
TOP: Write the converse of if-then statements.
KEY: Converse | If-Then Statements
28. ANS: D
The inverse is negating both the hypothesis and conclusion of the conditional.
Feedback
A
B
C
D
Is that the converse?
Remember
.
Remember
.
Correct!
PTS: 1
DIF: Average
REF: Lesson 2-3
OBJ: 2-3.3 Write the inverse of if-then statements.
NAT: NCTM RP.3
STA: 3.3.4
TOP: Write the inverse of if-then statements.
KEY: Inverse | If-Then Statements
29. ANS: D
Coplanar segments that do not intersect are parallel.
Feedback
A
B
C
D
Parallel lines do not intersect.
Parallel lines are coplanar.
Those segments are parallel to which line?
Correct!
PTS: 1
DIF: Average
REF: Lesson 3-1
OBJ: 3-1.1 Identify the relationships between two lines or two planes.
NAT: NCTM GM.1 | NCTM GM.1a
STA: 1.3.1
TOP: Identify the relationships between two lines or two planes.
KEY: Relationship Between Two Lines | Relationship Between Two Planes
30. ANS: B
Planes intersect in a line.
Feedback
A
B
C
D
Do they all intersect plane CHG in a line?
Correct!
Is that all?
Do they all intersect plane CHG in a line?
PTS:
OBJ:
NAT:
TOP:
KEY:
31. ANS:
1
DIF: Average
REF: Lesson 3-1
3-1.1 Identify the relationships between two lines or two planes.
NCTM GM.1 | NCTM GM.1a
STA: 1.3.1
Identify the relationships between two lines or two planes.
Relationship Between Two Lines | Relationship Between Two Planes
A
The formula for slope is
.
Feedback
A
B
C
D
Correct!
You are not solving for the slope of the perpendicular.
Remember y over x.
Subtract y1 from y2 and x1 from x2.
PTS:
NAT:
TOP:
32. ANS:
1
DIF: Basic
REF: Lesson 3-3
OBJ: 3-3.1 Find slopes of lines.
NCTM GM.1b | NCTM GM.2 | NCTM GM.2a
STA: 1.3.5 | 1.5.2
Find slopes of lines.
KEY: Slope | Slope of Lines
C
The formula for slope is
. If the slopes are the same they are parallel. If the product of the two slopes is
–1, they are perpendicular.
Feedback
A
B
C
Parallel slopes are the same and perpendicular ones are opposite reciprocals.
Parallel slopes are the same and perpendicular ones are opposite reciprocals.
Correct!
PTS:
OBJ:
NAT:
TOP:
KEY:
33. ANS:
1
DIF: Average
REF: Lesson 3-3
3-3.2 Use slope to identify parallel and perpendicular lines.
NCTM AL.2 | NCTM AL.2c | NCTM RE.2
STA: 1.3.5 | 1.5.2
Use slope to identify parallel lines and perpendicular lines.
Parallel Lines | Perpendicular Lines | Slope
C
The formula for slope is
. If the slopes are the same, the lines are parallel. If the product of the two
slopes is –1, the lines are perpendicular.
Feedback
A
B
C
Parallel slopes are the same and perpendicular ones are opposite reciprocals.
Parallel slopes are the same and perpendicular ones are opposite reciprocals.
Correct!
PTS: 1
DIF: Average
REF: Lesson 3-3
OBJ: 3-3.2 Use slope to identify parallel and perpendicular lines.
NAT: NCTM AL.2 | NCTM AL.2c | NCTM RE.2
STA: 1.3.5 | 1.5.2
TOP: Use slope to identify parallel lines and perpendicular lines.
KEY: Parallel Lines | Perpendicular Lines | Slope
34. ANS: C
The slope-intercept form is
.
Feedback
A
B
C
D
Which number is the slope?
What is the y-intercept?
Correct!
Remember y = mx + b.
PTS: 1
DIF: Basic
REF: Lesson 3-4
OBJ: 3-4.1 Write an equation of a line given information about its graph.
NAT: NCTM AL.2
STA: 1.5.2
TOP: Write an equation of a line given information about its graph.
KEY: Equation of Lines | Graphs
35. ANS: D
The point-slope form is
. Point
is a point through which the line passes.
Feedback
A
B
C
D
Is that point-slope form?
What is the slope?
Remember the point is (x1, y1).
Correct!
PTS:
OBJ:
STA:
KEY:
36. ANS:
1
DIF: Basic
REF: Lesson 3-4
3-4.2 Solve problems by writing equations.
NAT: NCTM GM.1 | NCTM GM.1b
1.5.6
TOP: Solve problems by writing equations.
Solve Problems | Write Equations
D
The point-slope form is
. Point
is a point through which the line passes.
Feedback
A
B
C
D
Is that point-slope form?
What is the slope?
Remember the point is (x1, y1).
Correct!
PTS: 1
DIF: Average
REF: Lesson 3-4
OBJ: 3-4.2 Solve problems by writing equations.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 1.5.6
TOP: Solve problems by writing equations.
KEY: Solve Problems | Write Equations
37. ANS: C
Postulates and theorems:
If corresponding angles are congruent, then lines are parallel.
If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the
given line.
If alternate exterior angles are congruent, then lines are parallel.
If consecutive interior angles are supplementary, then lines are parallel.
If alternate interior angles are congruent, then lines are parallel.
If two lines are perpendicular to the same line, then lines are parallel.
Feedback
A
B
C
D
What kind of angles are those?
What kind of angles are those?
Correct!
Which lines are parallel?
PTS: 1
DIF: Basic
REF: Lesson 3-5
OBJ: 3-5.1 Recognize angle conditions that occur with parallel lines.
NAT: NCTM GM.1b | NCTM GM.1c | NCTM RP.3
STA: 1.5.2
TOP: Recognize angle conditions that occur with parallel lines.
KEY: Angles | Parallel Lines
38. ANS: C
Postulates and theorems:
If corresponding angles are congruent, then lines are parallel.
If given a line and a point not on the line, then there exists exactly one line through the point that is parallel to the
given line.
If alternate exterior angles are congruent, then lines are parallel.
If consecutive interior angles are supplementary, then lines are parallel.
If alternate interior angles are congruent, then lines are parallel.
If two lines are perpendicular to the same line, then lines are parallel.
Feedback
A
B
C
D
What kind of angles are those?
What kind of angles are those?
Correct!
Which lines are parallel?
PTS: 1
DIF: Average
REF: Lesson 3-5
OBJ: 3-5.1 Recognize angle conditions that occur with parallel lines.
NAT: NCTM GM.1b | NCTM GM.1c | NCTM RP.3
STA: 1.5.2
TOP: Recognize angle conditions that occur with parallel lines.
KEY: Angles | Parallel Lines
39. ANS: C
The Angle Sum Theorem states that the sum of the measures of the angles of a triangle is 180.
Feedback
A
B
C
D
What do you know about vertical angles?
What do you know about vertical angles?
Correct!
Use the Angle Sum Theorem.
PTS: 1
DIF: Basic
REF: Lesson 4-2
OBJ: 4-2.1 Apply the Angle Sum Theorem.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 1.3.1
TOP: Apply the Angle Sum Theorem.
KEY: Angle Sum Theorem
40. ANS: C
The Exterior Angle Theorem states that the measure of an exterior angle of a triangle is equal to the sum of the
measures of the two remote interior angles.
Feedback
A
B
C
D
What is the sum of the measures of the angles in a triangle?
Did you use the Exterior Angle Theorem?
Correct!
Use the Exterior Angle Theorem.
PTS: 1
DIF: Average
REF: Lesson 4-2
OBJ: 4-2.2 Apply the Exterior Angle Theorem.
NAT: NCTM GM.1 | NCTM GM.1b
STA: 1.3.1
TOP: Apply the Exterior Angle Theorem.
KEY: Exterior Angle Theorem
41. ANS: C
The corresponding sides and angles can be determined from any congruence statement by following the order of
the vertices.
Feedback
A
B
C
D
The corresponding sides and angles can be determined from any congruence statement
by following the order of the vertices.
The corresponding sides and angles can be determined from any congruence statement
by following the order of the vertices.
Correct!
Did you follow the order of the vertices?
PTS: 1
DIF: Basic
REF: Lesson 4-3
OBJ: 4-3.1 Name and label corresponding parts of congruent triangles.
NAT: NCTM GM.1 | NCTM GM.1b | NCTM GM.3
STA: 1.3.3
TOP: Name and label corresponding parts of congruent triangles.
KEY: Corresponding Parts | Congruent Triangles
42. ANS: C
The vertices naming the triangles correspond to the congruent vertices of the two triangles in the same order.
Feedback
A
B
C
D
The letters naming the triangles correspond to the congruent vertices of the two
triangles.
Be careful with the order of the vertices.
Correct!
Are the vertices in the correct order?
PTS: 1
DIF: Average
REF: Lesson 4-3
NAT: NCTM GM.1 | NCTM GM.1b
STA: 1.3.3
KEY: Transformations | Congruence Transformations
OBJ: 4-3.2 Identify congruent transformations.
TOP: Identify congruent transformations.
SHORT ANSWER
43. ANS:
and
form a pair of consecutive interior angles and are thus supplementary. Therefore,
PTS: 1
DIF: Basic
REF: Lesson 3-2
OBJ: 3-2.3 Solve multi-step problems.
NAT: NCTM AL.2c | NCTM ME.1 | NCTM AL.4a | NCTM GM.2 | NCTM GM.2a
STA: 1.3.1 | 1.2.2 TOP: Solve multi-step problems.
KEY: Solve multi-step problems.
44. ANS:
The slope-intercept form of a linear equation is
where m is the slope of the line and b is the
y-intercept.
Use the point-slope form and either point to write the equation.
are the coordinates of any point on the line and
is the slope of the line.
PTS: 1
DIF: Basic
REF: Lesson 3-4
OBJ: 3-4.3 Solve multi-step problems.
NAT: NCTM AL.2 | NCTM GM.1 | NCTM GM.1b
STA: 1.5.2 | 1.5.6
TOP: Solve multi-step problems.
KEY: Solve multi-step problems.