Name____________________________
Date________________
Period__________
SECONDARY MATH I – BENCHMARK 3 (Units 6, 7, 8)
PART I – MULTIPLE CHOICE
DIRECTIONS: PLEASE CIRCLE THE CORRECT RESPONSE
1) Which of the following is the precise definition for a circle?
a. The set of all points equidistant from a point called the center.
b. A shape formed by two rays with a common endpoint called the vertex
c. Two endpoints of a line segment and all the points between them.
d. Lines that intersect to form a right angle.
2) Describe the transformation that takes point (𝑥, 𝑦) to point (𝑥 − 3, 𝑦 + 5).
a. Translate right 3 and up 5
b. Translate right 3 and down 5
c. Translate left 3 and up 5
d. Translate left 3 and down 5
3) How many lines of symmetry does a square have?
a. 2
b. 4
c. 6
d. Infinitely many
4) Which of the following counter-clockwise rotations about the center of the figure
will carry the rectangle displayed below onto itself?
a. 90 degrees
b. 180 degrees
c. 270 degrees
d. 300 degrees
5) Which transformation would carry figure 1 onto figure 2?
a. Rotation
b. Reflection
c. Dilation
d. Translation
6) What transformation is not a rigid motion
a. Rotation
b. Reflection
c. Dilation
d. Translation
7) Which two rigid motion transformations could be
used to prove quadrilateral ABCD is congruent to
quadrilateral KLMN?
a.
b.
c.
d.
Reflection over the y-axis, translation
Rotation about the origin, translation
Translation, reflection over the x-axis
Reflection, over the x-axis, reflection over the
y-axis
8) Which of the following show the figure (to the right)
reflected over the x-axis?
a.
c.
b.
d.
̅̅̅̅
9) Which side of trapezoid JKHI corresponds to 𝐴𝐵
a. ̅̅̅̅
𝐻𝐾
b. ̅̅̅
𝐽𝐾
̅̅̅
c. ̅𝐻𝐼
̅
d. 𝐼𝐽
10) Which method of proving triangle congruency is missing from the following list:
ASA, SSS, SAA?
a. AAA
b. SAS
c. SSA
d. No method is missing
11) Which triangle congruence can be used to
prove that the two triangles are congruent?
a. AAS
b. SSS
c. SAS
d. SSA
12) What additional information is required in
order to know that the triangles are congruent
by ASA?
̅̅̅̅
a. ̅̅̅̅
𝐻𝐺 ≅ 𝐶𝐵
̅̅̅̅ ≅ 𝐴𝐶
̅̅̅̅
b. 𝐻𝐺
̅̅̅̅
c. ̅̅̅̅
𝐹𝐻 ≅ 𝐶𝐵
̅̅̅̅ ≅ 𝐴𝐵
̅̅̅̅
d. 𝐹𝐺
13) Given ∆NOP, what construction was
performed?
a. Copy a segment
b. Copy an angle
c. Perpendicular bisector
d. Angle bisector
14) Given vertices at (−5, −1), (3,3), and
(6, −3), what would be the fourth vertex
be in order for the shape to be a rectangle?
a. (−2, −6)
b. (−2,6)
c. (−3,7)
d. (−2, −7)
15) A line contains the points (−3,5) and is parallel to the line 𝑦 = −2𝑥 + 7. What is
the equation of the line?
a. 𝑦 = −2𝑥 + 8
b. 𝑦 = −2𝑥 − 1
c. 𝑦 = −2𝑥 + 1
d. 𝑦 = −2𝑥 + 11
16) Given the line: 𝑦
1
= − 𝑥 − 7, what is the slope of a line parallel to it and the
2
slope of a line perpendicular to it?
1
a. Parallel
𝑚=−
2
b. Parallel
𝑚=2
1
c. Parallel
𝑚=−
d. Parallel
𝑚 = −2
2
17) What is the perimeter of the triangle to
nearest whole number?
a. 12 units
b. 18 units
c. 40 units
d. 50 units
perpendicular
𝑚 = −2
perpendicular
𝑚=
perpendicular
𝑚=2
perpendicular
𝑚=
1
2
1
2
18) Given a function, 𝑓(𝑥), describe what happens to the graph of the function when
it is replaced by 𝑓(𝑥 + 2).
a. Translate left 2 units
b. Translate right 2 units
c. Translate up 2 units
d. Translate down 2 units
19) 𝑓 (𝑥 ) = 6𝑥
intercept?
a.
b.
c.
d.
− 3 under goes a vertical translation of −4, what is the new y-
2
−1
−7
21
20) Given the function, 𝑓(𝑥) = −(3𝑥 ) + 𝑘 ,
(displayed on the right) find the value of 𝑘.
a. −3
b. 1
c. 3
d. 4
Name____________________________
Date________________
Period__________
SECONDARY MATH I – BENCHMARK 3 (Units 6, 7, 8)
PART II – CONSTRUCTED RESPONSE
DIRECTIONS: WRITE YOUR ANSWERS IN THE SPACES PROVIDED
1) Construct the bisector of the angle below. (3pts)
2) Given quadrilateral PQRS:
a. Create P’Q’R’S’ by transforming
quadrilateral PQRS according to the
rule (𝑥 + 3, 𝑦 + 5). List the
coordinates of the new vertices of
P’Q’R’S’. (4pts)
b. Describe the transformation. (2pts)
c. Prove that PQRS is a Parallelogram. (2pts)
d. Is Parallelogram P’Q’R’S’ a rectangle, square and/or rhombus? Justify
your answer. (2pts)
3) Refer to the figure on the right for the
following questions:
a. What transformation maps ∆𝐴𝐵𝐶 onto
∆𝐷𝐸𝐹? (1pt)
b. Is ∠𝐵 ≅ ∠𝐸? How do you know?
(2pts)
̅̅̅̅ ≅ ̅̅̅̅
c. Is 𝐵𝐶
𝐸𝐹 ? How do you know? (2pts)
d. Is ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐷𝐸 ? How do you know? (2pts)
e. Is ∆𝐴𝐵𝐶 ≅ ∆𝐷𝐸𝐹? What triangle congruency criterion proves it? (2pts)
PART I - MULTIPLE CHOICE ANSWERS
QUESTION
ANSWER
STANDARD
QUESTION
ANSWER
STANDARD
1
A
G.CO.1
11
C
G.CO.8
2
C
G.CO.2
12
A
G.CO.8
3
B
G.CO.3
13
C
G.CO.12
4
B
G.CO.3
14
D
G.GPE.4
5
D
G.CO.5
15
B
G.GPE.5
6
C
G.CO.6
16
C
G.GPE.5
7
A
G.CO.6
17
C
G.GPE.7
8
A
G.CO.5
18
A
F.BF.3
9
A
G.CO.7
19
C
F.BF.3
10
B
G.CO.8
20
D
F.BF.3
PART II – CONSTRUCTED RESPONSE ANSWERS
QUESTION 1
ANSWER
STANDARD
POINTS
G.CO.12
Construct the angle
bisector
3 points
QUESTION 2
ANSWER
STANDARD
POINTS
a.
G.CO.5
Transform figures
4 points
𝑃’ (1,7), 𝑄’ (4,3), 𝑅’ (1, −1), 𝑆’ (−2,3)
b.
G.CO.2
right three and up five
Describe Transformation
2 points
c. BE CONSIDERATE OF OTHER
POSSIBLE PROOFS.
4
𝑚𝑃𝑄 = 𝑚𝑆𝑅 = −
3
4
𝑚𝑃𝑆 = 𝑚𝑄𝑅 =
3
Because PQRS is a quadrilateral with
opposite sides parallel, it is a
G.CO.1
Precise definitions
G.GPE.4
2 points
Use coordinates to prove
simple geometric
theorems algebraically
parallelogram.
d.
G.CO.1
𝑑𝑃𝑄 = 𝑑𝑆𝑅 = 𝑑𝑃𝑆 = 𝑑𝑄𝑅 = 5
Precise definitions
Since all four sides are the same length
and opposite sides are parallel it is a
G.GPE.4
RHOMBUS. It is not a square since the
Use coordinates to prove
slope of the adjacent lines are not
simple geometric
opposite reciprocals.
theorems algebraically
2 points
QUESTION 3
ANSWER
a.
(−𝑥, −𝑦)
A 180 degree rotation with the
origin as the center of rotation
b.
yes, because a rotation is a rigid
motion transformation that
preserves angle measurement
c.
yes, because a rotation is a rigid
motion transformation that
preserves length
d.
yes, because a rotation is a rigid
motion transformation that
preserves length
e.
yes, by SAS congruency
STANDARD
POINTS
G.CO.2
Represent transformations in the
1 point
coordinate plane
G.CO.6
Definition of congruence in terms
2 points
of rigid motion
G.CO.6
Definition of congruence in terms
2 points
of rigid motion
G.CO.6
Definition of congruence in terms
2 points
of rigid motion
G.CO.7
Show that two triangles are
congruent
2 points