Download Geometry - Benchmark II

Geometry - Benchmark II
Multiple Choice (3 pts. each)
____
1. If Z is the midpoint of
R
what are x, RZ, and RT?
Z
T
4 x - 28
24
a. x = 13, RZ = 48, and RT = 24
b. x = 11, RZ = 16, and RT = 32
____
c. x = 13, RZ = 24, and RT = 48
d. x = 15, RZ = 24, and RT = 48
2. Based on the pattern, what are the next two terms of the sequence?
,...
____
a.
c.
b.
d.
3. What is the relationship between
1
and
?
2
m
3
4
5
6
n
7
8
a. corresponding angles
b. same-side interior angles
____
c. alternate interior angles
d. alternate exterior angles
4. Find the sum of the measures of the angles of the figure.
a. 900
b. 1080
c. 1620
d. 1260
____
5. Find the missing values of the variables. The diagram is not to scale.
125°
x°
y°
124°
65°
a. x = 124, y = 125
b. x = 56, y = 114
____
c. x = 114, y = 56
d. x = 56, y = 124
6. Find the values of the variables in the parallelogram. The diagram is not to scale.
29
102
y°
z°
x°
a.
b.
____
c.
d.
7. ABCD is a parallelogram. If
A
D
____
then
The diagram is not to scale.
B
C
a. 66
b. 124
c. 114
d. 132
a.
b.
c.
d.
8.
____
9. The two triangles are congruent as suggested by their appearance. Find the value of c. The diagrams are not to
scale.
d°
38°
g
5
b
f°
4
e°
52°
3
c
a. 4
b. 5
c. 3
d. 38
____ 10. Which triangles are congruent by ASA?
F
A
(
V
T ))
((
B
(
)
G
H
U
C
a.
b.
c.
d. none
____ 11. What is the value of x?
xº
56°
Drawing not to scale
a. 68°
____ 12. Find the value of x.
b. 62°
c. 112°
d. 124°
16
3x – 4
a. 4
b. 8
c.
6.6
d. 6
____ 13. Use the information in the diagram to determine the measure of the angle formed by the line from the point on
the ground to the top of the building and the side of the building. The diagram is not to scale.
46º
a. 46º
____ 14.
b. 23º
bisects
c. 92º
d. 44º
Find the value of x. The diagram is not to scale.
E
|
|
8x + 42
F
)
15x
)
30°
D
a.
23
42
G
b. 90
c. 30
d. 6
____ 15. List the sides in order from shortest to longest. The diagram is not to scale.
J
66°
50°
K
64°
L
a.
b.
c.
d.
Short Answer (5 pts. each)
16. Can these three segments form the sides of a triangle? Explain.
c
b
a
17. Identify parallel segments in the diagram.
C
8
6
B
D
8
6
A
5
F
5
E
Essay
18. AC and BD are perpendicular bisectors of each other. Find BC, AE, DB, and DC. Justify your answers.
A
13
12
D
E
B
5
C
19. Find the values of the variables. Show your work and explain your steps. The diagram is not to scale.
o
31
x
w
v
y
68o
z
Geometry - Benchmark II
Answer Section
MULTIPLE CHOICE
1. ANS:
OBJ:
TOP:
DOK:
2. ANS:
REF:
OBJ:
TOP:
DOK:
3. ANS:
OBJ:
NAT:
KEY:
4. ANS:
REF:
OBJ:
NAT:
KEY:
5. ANS:
REF:
OBJ:
NAT:
KEY:
6. ANS:
OBJ:
NAT:
KEY:
DOK:
7. ANS:
OBJ:
NAT:
KEY:
8. ANS:
OBJ:
NAT:
KEY:
9. ANS:
OBJ:
NAT:
KEY:
10. ANS:
REF:
OBJ:
NAT:
C
PTS: 1
DIF: L3
REF: 1-3 Measuring Segments
1-3.1 Find and compare lengths of segments NAT:
G.3.b
1-3 Problem 4 Using the Midpoint KEY: segment | segment length | midpoint
DOK 2
B
PTS: 1
DIF: L3
2-1 Patterns and Inductive Reasoning
2-1.1 Use inductive reasoning to make conjectures
NAT: G.5.a
2-1 Problem 1 Finding and Using a Pattern
KEY: pattern | inductive reasoning
DOK 2
C
PTS: 1
DIF: L3
REF: 3-1 Lines and Angles
3-1.2 Identify angles formed by two lines and a transversal
M.1.d| G.3.g TOP: 3-1 Problem 3 Classifying an Angle Pair
angle pair | transversal
DOK: DOK 1
A
PTS: 1
DIF: L2
6-1 The Polygon Angle-Sum Theorems
6-1.1 Find the sum of the measures of the interior angles of a polygon
M.1.d| G.3.f TOP: 6-1 Problem 1 Finding a Polygon Angle Sum
sum of angles of a polygon
DOK: DOK 1
C
PTS: 1
DIF: L3
6-1 The Polygon Angle-Sum Theorems
6-1.1 Find the sum of the measures of the interior angles of a polygon
M.1.d| G.3.f TOP: 6-1 Problem 3 Using the Polygon Angle-Sum Theorem
exterior angle | Polygon Angle-Sum Theorem
DOK: DOK 2
D
PTS: 1
DIF: L4
REF: 6-2 Properties of Parallelograms
6-2.1 Use relationships among sides and angles of parallelograms
G.1.c| G.3.f TOP: 6-2 Problem 1 Using Consecutive Angles
parallelogram | opposite angles | consecutive angles | transversal
DOK 2
C
PTS: 1
DIF: L2
REF: 6-2 Properties of Parallelograms
6-2.1 Use relationships among sides and angles of parallelograms
G.1.c| G.3.f TOP: 6-2 Problem 1 Using Consecutive Angles
parallelogram | consecutive angles DOK: DOK 1
D
PTS: 1
DIF: L2
REF: 4-1 Congruent Figures
4-1.1 Recognize congruent figures and their corresponding parts
G.2.e| G.3.e TOP: 4-1 Problem 1 Finding Congruent Parts
congruent figures | corresponding parts
DOK: DOK 1
C
PTS: 1
DIF: L3
REF: 4-1 Congruent Figures
4-1.1 Recognize congruent figures and their corresponding parts
G.2.e| G.3.e TOP: 4-1 Problem 2 Using Congruent Parts
congruent figures | corresponding parts
DOK: DOK 2
B
PTS: 1
DIF: L2
4-3 Triangle Congruence by ASA and AAS
4-3.1 Prove two triangles congruent using the ASA Postulate and the AAS Theorem
G.2.e| G.3.e| G.5.e
TOP: 4-3 Problem 1 Using ASA
KEY:
11. ANS:
REF:
OBJ:
NAT:
KEY:
DOK:
12. ANS:
OBJ:
TOP:
DOK:
13. ANS:
OBJ:
TOP:
KEY:
DOK:
14. ANS:
REF:
OBJ:
NAT:
KEY:
15. ANS:
OBJ:
NAT:
DOK:
ASA
DOK: DOK 1
A
PTS: 1
DIF: L2
4-5 Isosceles and Equilateral Triangles
4-5.1 Use and apply properties of isosceles and equilateral triangles
G.1.c| G.2.e| G.3.e
TOP: 4-5 Problem 2 Using Algebra
isosceles triangle | Isosceles Triangle Theorem | Triangle Angle-Sum Theorem | word problem
DOK 2
A
PTS: 1
DIF: L3
REF: 5-1 Midsegments of Triangles
5-1.1 Use properties of midsegments to solve problems
NAT: G.3.c
5-1 Problem 2 Finding Lengths
KEY: midpoint | midsegment | Triangle Midsegment Theorem
DOK 2
A
PTS: 1
DIF: L3
REF: 5-1 Midsegments of Triangles
5-1.1 Use properties of midsegments to solve problems
NAT: G.3.c
5-1 Problem 3 Using a Midsegment of a Triangle
midsegment | Triangle Midsegment Theorem | problem solving
DOK 1
D
PTS: 1
DIF: L3
5-2 Perpendicular and Angle Bisectors
5-2.1 Use properties of perpendicular bisectors and angle bisectors
G.3.c
TOP: 5-2 Problem 3 Using the Angle Bisector Theorem
Angle Bisector Theorem | angle bisector
DOK: DOK 2
C
PTS: 1
DIF: L3
REF: 5-6 Inequalities in One Triangle
5-6.1 Use inequalities involving angles and sides of triangles
G.3.c
TOP: 5-6 Problem 3 Using Theorem 5-11
DOK 1
SHORT ANSWER
16. ANS:
No; for three segments to form the sides of a triangle, the sum of the length of two segments must be greater
than the length of the third segment.
PTS:
OBJ:
NAT:
KEY:
17. ANS:
PTS:
OBJ:
TOP:
KEY:
DOK:
1
DIF: L3
REF: 5-6 Inequalities in One Triangle
5-6.1 Use inequalities involving angles and sides of triangles
G.3.c
TOP: 5-6 Problem 4 Using the Triangle Inequality Theorem
Triangle Inequality Theorem
DOK: DOK 1
1
DIF: L2
REF: 5-1 Midsegments of Triangles
5-1.1 Use properties of midsegments to solve problems
NAT: G.3.c
5-1 Problem 1 Identifying Parallel Segments
midsegment | parallel lines | Triangle Midsegment Theorem
DOK 1
ESSAY
18. ANS:
[4]
BC = 13 by the Perpendicular Bisector Theorem.
[3]
[2]
[1]
AE = 5 by the Perpendicular Bisector Theorem.
BE = 12 by the Perpendicular Bisector Theorem, so DB = DE + BE = 12 + 12 = 24.
by SAS, so DC = BC = 13.
finds three lengths with correct explanations
finds two lengths with correct explanations
finds one length with correct explanation
PTS: 1
DIF: L3
REF: 5-2 Perpendicular and Angle Bisectors
OBJ: 5-2.1 Use properties of perpendicular bisectors and angle bisectors
NAT: G.3.c
TOP: 5-2 Problem 1 Using the Perpendicular Bisector Theorem
KEY: extended response | rubric-based question | reasoning | perpendicular bisector | Perpendicular Bisector
Theorem
DOK: DOK 2
19. ANS:
[4] w + 31 + 90 = 180, so w = 59º. Because vertical angles are congruent, y = 59º. Because
supplementary angles have measures with sum 180, x = v = 121º.
z + 68 + y = z + 68 + 59 = 180, so z = 53º.
[3] small error leading to one incorrect answer
[2] three correct answers, work shown
[1] two correct answers, work shown
PTS: 1
DIF: L3
REF: 3-5 Parallel Lines and Triangles
OBJ: 3-5.1 Use parallel lines to prove a theorem about triangles
NAT: M.1.d| G.3.g TOP: 3-5 Problem 2 Using the Triangle Exterior Angle Theorem
KEY: Triangle Angle-Sum Theorem | exterior angles theorem | vertical angles | supplementary angles |
extended response | rubric-based question DOK: DOK 3