Download Fall Geometry Final Review Answer Section

Fall Geometry Final Review
Short Answer
1. When a conditional and its converse are true, you can combine them as a true ____.
2. Write the two conditional statements that make up the following biconditional.
I drink juice if (and only if) it is breakfast time.
3. Is the following definition of dog reversible? If yes, write it as a true biconditional.
A dog is a mammal.
4. One way to show that a statement is NOT a good definition is to find a ____.
5. Are C, B, and A collinear? If so, name the line on which they lie.
C
B
D
A
6. What is the name of the ray that is opposite
H
G
F
E
7. Complete the two-column proof.
Given:
Prove:
?
8. Let p be “you are a senior” and let q be “you are in high school.” Write the converse. Then decide whether it
is true or false.
9. If
, find the value of FG. The drawing is not to scale.
E
F
G
10. If
, find the value of x. The drawing is not to scale.
E
F
G
11. Find the value of x.
(6x + 12)°
108°
12. Based on the pattern, what are the next two terms of the sequence?
2, 6, 10, 14, . . .
13. If possible, use the Law of Detachment to draw a conclusion from the two given statements. If not possible,
write not possible.
Statement 1: If x = 3, then 2x – 9 = –3.
Statement 2: x = 3
14. Use the Law of Syllogism to draw a conclusion from the two given statements.
If it is Thursday, then Sara gets a paycheck.
If Sara gets a paycheck, then she goes to the bank.
15. If
and point F is 2/5 of the way between E and G, find the value FG.
The drawing is not to scale.
E
F
16. What is the relationship between
G
and
?
1
2
m
3
4
5
6
n
7
8
17. Line r is parallel to line t. Find m 6. The diagram is not to scale.
r
7
137°
1
3
t
4
2
5
6
18. Find the coordinates of the midpoint of the segment whose endpoints are H(2, 15) and K(8, 5).
19. Find the distance between points P(2, 3) and Q(9, 4) to the nearest tenth.
20. Find the image of C under the translation described by the translation rule
E8
y
A
4
C
–8
.
–4
4
–4
8 x
D
B
–8
21. The vertices of a triangle are P(2, –8), Q(–1, 2), and R(1, 2). Name the vertices of a triangle reflected over the
x axis.
22. Is
a vertical compression or a vertical stretch? What coordinate rule maps
?
to
y
A'
A
–8
B'
8
4
B
–4
4
8
x
C
–4
–8
C'
23. Which two triangles similar? How do you know?
24.
25. State whether
and
5
26. What is the value of x?
are congruent. Justify your answer.
5
36°
21
21
xº
Drawing not to scale
27. What additional information will allow you to prove the triangles congruent by the HL Theorem?
A
B
|
C
|
D
E
28. What is the geometric mean of 81 and 4
29. What is the value of x, given that
?
A
x
8
P
Q
32
24
B
C
30. What is value of x, given that
O
P
9
N
x
Q
18
20
M
?
31.
is a right triangle with altitude to the hypotenuse
. What is the geometric mean of JM and KM?
L
J
M
K
32. What is the value of x?
xº
58°
Drawing not to scale
33. B is the midpoint of
D is the midpoint of
and AE = 29. Find BD. The diagram is not to scale.
C
B
A
34.
bisects
D
E
Find the value of x. The diagram is not to scale.
|
|
E
2x + 60
F
)
5x
)
28°
D
G
35. Where is the circumcenter of any given triangle?
36. Find the length of
, given that
is a median of the triangle and AC = 50.
D
A
B
C
37. Name the point of concurrency of the angle bisectors.
38. For a triangle, list the respective names of the points of concurrency of
• perpendicular bisectors of the sides
• bisectors of the angles
• medians
• lines containing the altitudes
39. Find the values of x, y, and z. The diagram is not to scale.
46°
18°
65°
x°
z°
y°
40. Find the value of x. The diagram is not to scale.
43°
112°
x°
41. Construct a segment bisector
42.
43. Construct a pair of parallel lines
44. Construct a line perpendicular through point F
45.
46. Describe the rule
in words
47. Write a two column proof
48. Graph the reflection of the triangle over the x-axis.
49.
Fall Geometry Final Review
Answer Section
SHORT ANSWER
1. ANS:
biconditional
PTS: 1
DIF: L2
REF: 2-3 Biconditionals and Definitions
OBJ: 2-3.1 To write biconditionals and recognize good definitions
STA: (4)(A)| (4)(B)
TOP: 2-3 Problem 1 Writing a Biconditional
KEY: conditional statement | biconditional statement
2. ANS:
If I drink juice, then it is breakfast time.
If it is breakfast time, then I drink juice.
PTS: 1
DIF: L3
REF: 2-3 Biconditionals and Definitions
OBJ: 2-3.1 To write biconditionals and recognize good definitions
STA: (4)(A)| (4)(B)
TOP: 2-3 Problem 2 Identifying the Conditionals in a Biconditional
KEY: biconditional statement | conditional statement
3. ANS:
The reverse is false.
PTS: 1
DIF: L3
REF: 2-3 Biconditionals and Definitions
OBJ: 2-3.1 To write biconditionals and recognize good definitions
STA: (4)(A)| (4)(B)
TOP: 2-3 Problem 3 Writing a Definition as a Biconditional
KEY: biconditional statement
4. ANS:
counterexample
PTS: 1
DIF: L2
REF: 2-3 Biconditionals and Definitions
OBJ: 2-3.1 To write biconditionals and recognize good definitions
STA: (4)(A)| (4)(B)
TOP: 2-3 Problem 4 Identifying Good Definitions
KEY: counterexample
5. ANS:
Yes, they lie on the line AC.
PTS:
OBJ:
STA:
KEY:
6. ANS:
1
DIF: L2
REF: 1-1 Points, Lines, and Planes
1-1.1 To understand basic terms and postulates of geometry
(4)(A)
TOP: 1-1 Problem 1 Naming Points, Lines, and Planes
point | line | collinear points
PTS:
OBJ:
STA:
KEY:
1
DIF: L2
REF: 1-1 Points, Lines, and Planes
1-1.1 To understand basic terms and postulates of geometry
(4)(A)
TOP: 1-1 Problem 2 Naming Segments and Rays
ray | opposite rays
7. ANS:
a. Given
b. Subtraction Property of Equality
c. Multiplication Property of Equality
PTS: 1
DIF: L2
REF: 2-5 Reasoning in Algebra and Geometry
OBJ: 2-5.1 To connect reasoning in algebra and geometry
STA: (6)(A)
TOP: 2-5 Problem 3 Writing a Two-Column Proof
KEY: Properties of Equality | proof | Two-column Proof
8. ANS:
If you are in high school, then you are a senior; false
PTS: 1
STA: G.4.B
NOT: Example 3
9. ANS:
15
DIF: Level 2
REF: Geometry Sec. 2.1
KEY: conditional statement | converse | inverse | contrapositive | application
PTS: 1
DIF: L2
REF: 1-2 Measuring Segments
OBJ: 1-2.1 To find and compare lengths of segments
STA: (2)(A)
TOP: 1-2 Problem 2 Using the Segment Addition Postulate
KEY: coordinate | distance
10. ANS:
PTS: 1
DIF: L3
REF: 1-2 Measuring Segments
OBJ: 1-2.1 To find and compare lengths of segments
STA: (2)(A)
TOP: 1-2 Problem 2 Using the Segment Addition Postulate
KEY: coordinate | distance
11. ANS:
PTS: 1
STA: G.6.A
12. ANS:
18, 22
DIF: Level 1
REF: Geometry Sec. 2.6
KEY: using angle relationships
NOT: Example 4-1
PTS: 1
DIF: L3
REF: 2-1 Patterns and Conjectures
OBJ: 2-1.1 To use inductive reasoning to make conjectures
STA: (4)(C)| (5)(A)
TOP: 2-1 Problem 1 Finding and Using a Pattern
KEY: pattern | inductive reasoning
13. ANS:
2x – 9 = –3
PTS: 1
DIF: L4
REF: 2-4 Deductive Reasoning
OBJ: 2-4.1 To use the Law of Detachment and the Law of Syllogism
STA: (6)(A)
TOP: 2-4 Problem 1 Using the Law of Detachment
KEY: Law of Detachment | deductive reasoning
14. ANS:
If it is Thursday, then Sara goes to the bank.
PTS: 1
DIF: L3
REF: 2-4 Deductive Reasoning
OBJ: 2-4.1 To use the Law of Detachment and the Law of Syllogism
STA: (6)(A)
TOP: 2-4 Problem 2 Using the Law of Syllogism
KEY: deductive reasoning | Law of Syllogism
15. ANS:
18
PTS: 1
DIF: L4
REF: 1-2 Measuring Segments
OBJ: 1-2.1 To find and compare lengths of segments
STA: (2)(A)
TOP: 1-2 Problem 2 Using the Segment Addition Postulate
KEY: coordinate | distance | partition segment in a given ratio
16. ANS:
corresponding angles
PTS:
OBJ:
STA:
KEY:
17. ANS:
43
1
DIF: L3
REF: 3-1 Lines and Angles
3-1.2 To identify angles formed by two lines and a transversal
(6)(A)
TOP: 3-1 Problem 3 Classifying an Angle Pair
angle pairs | transversal | parallel lines
PTS: 1
DIF: L3
REF: 3-2 Properties of Parallel Lines
OBJ: 3-2.2 To use properties of parallel lines to find angle measures
STA: (5)(A)| (6)(A)
TOP: 3-2 Problem 2 Identifying Supplementary Angles
KEY: parallel lines | alternate interior angles
18. ANS:
(5, 10)
PTS:
OBJ:
STA:
KEY:
19. ANS:
7.1
1
DIF: L2
REF: 5-1 Midpoint and Distance in the Coordinate Plane
5-1.1 To find the midpoint of a segment by deriving and using the midpoint formula
(2)(A)| (2)(B)
TOP: 5-1 Problem 2 Finding the Midpoint
coordinate plane | Midpoint Formula
PTS: 1
DIF: L3
REF: 5-1 Midpoint and Distance in the Coordinate Plane
OBJ: 5-1.2 To find the distance between two points in the coordinate plane by deriving and using the
distance formula
STA: (2)(A)| (2)(B)
TOP: 5-1 Problem 5 Finding Distance
KEY: Distance Formula | coordinate plane
20. ANS:
A
PTS: 1
DIF: L3
REF: 8-1 Translations
OBJ: 8-1.2 To find translation images of figures
STA: (3)(A)| (3)(C)| (6)(C)
TOP: 8-1 Problem 3 Finding the Image of a Translation
KEY: translation | preimage | image
21. ANS:
PTS: 1
DIF: L3
REF: 8-2 Reflections
OBJ: 8-2.1 To find reflection images of figures
STA: (3)(A)| (3)(C)
TOP: 8-2 Problem 1 Reflecting a Point Across a Line
KEY: reflection | line of reflection
22. ANS:
vertical stretch
PTS:
OBJ:
STA:
KEY:
23. ANS:
1
DIF: L3
REF: 8-8 Other Non-Rigid Transformations
8-8.2 To find compositions of transformations, including non-rigid transformations
(3)(A)| (3)(B)| (3)(C)
TOP: 8-8 Problem 2 Describing a Non-Rigid Transformation
compression | stretch
; SAS
PTS:
OBJ:
STA:
KEY:
24. ANS:
1
DIF: L4
REF: 9-3 Proving Triangles Similar
9-3.1 To use the AA Postulate and the SAS and SSS theorems
(7)(B)| (8)(A)
TOP: 9-3 Problem 2 Verifying Triangle Similarity
Side-Angle-Side Similarity Theorem
PTS: 1
DIF: L2
REF: 4-1 Congruent Figures
OBJ: 4-1.1 To recognize congruent figures and their corresponding sides and angles
STA: (6)(C)
TOP: 4-1 Problem 1 Finding Congruent Sides and Angles
KEY: congruent polygons | corresponding parts
25. ANS:
yes, by either SSS or SAS
PTS:
OBJ:
STA:
KEY:
26. ANS:
72°
1
DIF: L3
REF: 4-2 Triangle Congruence by SSS and SAS
4-2.1 To prove two triangles congruent using the SSS and SAS Postulates
(5)(A)| (5)(C)| (6)(B)
TOP: 4-2 Problem 4 Identifying Congruent Triangles
SSS | SAS | reasoning
PTS:
OBJ:
STA:
KEY:
27. ANS:
1
DIF: L2
REF: 4-5 Isosceles and Equilateral Triangles
4-5.1 To use and apply properties of isosceles and equilateral triangles
(5)(A)| (5)(C)| (6)(B)| (6)(D)
TOP: 4-5 Problem 4 Using Algebra
isosceles triangle | Converse of Isosceles Triangle Theorem | Triangle Angle-Sum Theorem
PTS:
OBJ:
STA:
KEY:
28. ANS:
18
1
DIF: L3
REF: 4-6 Congruence in Right Triangles
4-6.1 To prove right triangles congruent using the Hypotenuse-Leg Theorem
(6)(B)
TOP: 4-6 Problem 2 Writing a Proof Using the HL Theorem
hypotenuse | HL Theorem | right triangle | reasoning
PTS:
OBJ:
STA:
KEY:
29. ANS:
1
DIF: L2
REF: 9-4 Similarity in Right Triangles
9-4.1 To find and use relationships in similar right triangles
(7)(B)| (8)(A)| (8)(B)
TOP: 9-4 Problem 3 Finding the Geometric Mean
geometric mean | proportion
6
PTS:
OBJ:
STA:
TOP:
KEY:
30. ANS:
x = 10
1
DIF: L2
REF: 9-5 Proportions in Triangles
9-5.1 To use the Triangle Proportionality Theorem and the Triangle-Angle-Bisector Theorem
(5)(A)| (7)(B)| (8)(A)
9-5 Problem 3 Using the Triangle Proportionality Theorem
Side-Splitter Theorem
PTS:
OBJ:
STA:
TOP:
KEY:
31. ANS:
LM
1
DIF: L3
REF: 9-5 Proportions in Triangles
9-5.1 To use the Triangle Proportionality Theorem and the Triangle-Angle-Bisector Theorem
(5)(A)| (7)(B)| (8)(A)
9-5 Problem 3 Using the Triangle Proportionality Theorem
Side-Splitter Theorem
PTS:
OBJ:
STA:
KEY:
32. ANS:
64°
1
DIF: L3
REF: 9-4 Similarity in Right Triangles
9-4.1 To find and use relationships in similar right triangles
(7)(B)| (8)(A)| (8)(B)
TOP: 9-4 Problem 4 Identifying Proportions in a Right Triangle
geometric mean
PTS:
OBJ:
STA:
KEY:
33. ANS:
14.5
1
DIF: L2
REF: 4-5 Isosceles and Equilateral Triangles
4-5.1 To use and apply properties of isosceles and equilateral triangles
(5)(A)| (5)(C)| (6)(B)| (6)(D)
TOP: 4-5 Problem 4 Using Algebra
isosceles triangle | Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | word problem
PTS:
OBJ:
STA:
KEY:
34. ANS:
20
1
DIF: L2
REF: 5-2 Midsegments of Triangles
5-2.1 To use properties of midsegments to solve problems
(6)(D)
TOP: 5-2 Problem 3 Finding Lengths
midpoint | midsegment | Triangle Midsegment Theorem
PTS: 1
DIF: L3
REF: 5-3 Perpendicular and Angle Bisectors
OBJ: 5-3.1 To use properties of perpendicular bisectors and angle bisectors
STA: (5)(C)| (6)(A)
TOP: 5-3 Problem 5 Using the Angle Bisector Theorem
KEY: Angle Bisector Theorem | angle bisector
35. ANS:
the point of concurrency of the perpendicular bisectors of the sides of the triangle
PTS:
OBJ:
STA:
KEY:
1
DIF: L2
REF: 5-4 Bisectors in Triangles
5-4.1 To identify properties of perpendicular bisectors and angle bisectors
(5)(A)| (5)(C)| (6)(D)
TOP: 5-4 Problem 2 Finding the Circumcenter of a Triangle
point of concurrency | concurrent | circumcenter of a triangle
36. ANS:
25
PTS:
OBJ:
STA:
KEY:
37. ANS:
C
1
DIF: L2
REF: 5-5 Medians and Altitudes
5-5.1 To identify properties of medians and altitudes of a triangle
(6)(D)
TOP: 5-5 Problem 1 Finding the Length of a Median
median of a triangle
PTS: 1
DIF: L3
REF: 5-4 Bisectors in Triangles
OBJ: 5-4.1 To identify properties of perpendicular bisectors and angle bisectors
STA: (5)(A)| (5)(C)| (6)(D)
TOP: 5-4 Problem 4 Identifying and Using the Incenter of a Triangle
KEY: angle bisector | incenter of a triangle | point of concurrency
38. ANS:
circumcenter
incenter
centroid
orthocenter
PTS: 1
DIF: L3
REF: 5-5 Medians and Altitudes
OBJ: 5-5.1 To identify properties of medians and altitudes of a triangle
STA: (6)(D)
TOP: 5-5 Problem 3 Finding the Orthocenter
KEY: angle bisector | circumcenter of a triangle | centroid of a triangle | orthocenter of a triangle | median |
altitude of a triangle | perpendicular bisector
39. ANS:
PTS: 1
DIF: L3
REF: 3-5 Parallel Lines and Triangles
OBJ: 3-5.1 To find measures of angles of triangles
STA: (6)(D)
TOP: 3-5 Problem 2 Using the Triangle Angle-Sum Theorem
KEY: triangle | sum of angles of a triangle
40. ANS:
69
PTS:
OBJ:
TOP:
KEY:
41. ANS:
1
DIF: L2
REF: 3-5 Parallel Lines and Triangles
3-5.1 To find measures of angles of triangles
STA: (6)(D)
3-5 Problem 3 Using the Triangle Exterior Angle Theorem
triangle | sum of angles of a triangle | exterior angle of a polygon | remote interior angles
PTS: 1
42. ANS:
y+9=3(x+3)
PTS: 1
43. ANS:
PTS: 1
44. ANS:
PTS: 1
45. ANS:
PTS: 1
46. ANS:
PTS: 1
47. ANS:
PTS: 1
48. ANS:
graph
PTS: 1
49. ANS:
Angle C
PTS: 1