Geometry Unit #1 (geometry basics and transformations)
A) HSG-CO.A.1 Know precise definitions of angle, circle,
perpendicular line, parallel line, and line segment, based
on the undefined notions of point, line, distance along a
line, and distance around a circular arc.

B) HSG-CO.A.2 Represent transformations in the plane

using, e.g., transparencies and geometry software;
Compare transformations that preserve distance and
angle to those that do not (e.g., translation versus
horizontal stretch).

C)
HSG.CO.A.3 Given a rectangle, parallelogram,

trapezoid, or regular polygon, describe the rotations and
reflections that carry it onto itself.
I) HSG-GPE.B.6 Find the point on a directed line
segment between two given points that partitions the
segment in a given ratio.
D)
HSG-CO.A.4 Develop definitions of rotations,
reflections, and translations in terms of angles, circles,
perpendicular lines, parallel lines, and line segments.

E) HSG-CO.A.5 Given a geometric figure and a rotation,
reflection, or translation, draw the transformed figure
using, e.g., graph paper, tracing paper, or geometry
software. Specify a sequence of transformations that will
carry a given figure onto another.
F) HSG-CO.B.6 Use geometric descriptions of rigid
motions to transform figures and to predict the effect of a
given rigid motion on a given figure; given two figures,
use the definition of congruence in terms of rigid motions
to decide if they are congruent.

G) HSG-CO.D.12 Make formal geometric constructions

with a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding,
dynamic geometric software, etc.). Copying a segment;
copying an angle; bisecting a segment; bisecting an
angle; constructing perpendicular lines, including the
perpendicular bisector of a line segment; and
constructing a line parallel to a given line through a point
not on the line.

H) HSG-SRT.A.1 Verify experimentally the properties of
dilations given by a center and a scale factor:

HSG-SRT.A.1a A dilation takes a line not passing
through the center of the dilation to a parallel line, and
leaves a line passing through the center unchanged.
o
HSG-SRT.A.1b The dilation of a line segment is longer
or shorter in the ratio given by the scale factor.
*Distance Formula City Project
*3 Formative Quizzes
*1 Summative Test
Geometry Unit #1 (geometry basics and transformations)
1) I can recognize basic geometric shapes (square,
parallelogram, rhombus, diamond, trapezoid, isosceles triangle,
pentagon, hexagon, etc.).
2) I can define collinear and coplanar.
PROOF OF UNDERSTANDING:
PROOF OF UNDERSTANDING:
Collinear = _____________________________
Coplanar = _____________________________
3) I can identify and name the various parts of a circle (radius,
circumference, diameter, arc, etc.).
4) I can define the terms congruent and similar.
PROOF OF UNDERSTANDING:
PROOF OF UNDERSTANDING:
CONGRUENT =
SIMILAR =
Which shapes below are congruent? Which shapes are
similar?
J
A
C
G
Radius = ___________________________________________
D
Diameter = _________________________________________
Define circumference = _______________________________
What is an arc? _____________________________________
E
F
B
H
Geometry Unit #1 (geometry basics and transformations)
5) I can recognize and understand what proportional shapes
look like.
6) I can define the terms finite and infinite.
PROOF OF UNDERSTANDING:
PROOF OF UNDERSTANDING:
FINITE=
INFINITE=
What is the value of x?
7) You are snowboarding down a slope. Which of the following
8) Which of the following would be considered a true line, in
is consistently perpendicular?
geometric terms?
(A) Your leg and the board
(A) You, a few friends, and thousands of others
(B) Your leg and the slope
standing outside a stadium waiting for tickets to the
(C) Your arms, stretched out for balance, and the rest
hottest concert of the year
of your body
(B) The direction along which an astronomer is
(D) None of the above
looking through a telescope for a new planet
thought to be farther from Earth than Neptune
(C) The equator
(D) A row of cars, stuck in a traffic jam so long that
you can't see the end – neither in front, nor behind
you
9) Harry Potter and the Sorcerer's Stone. The night of the big
10) If you ride the elevator from the lobby of the Empire State
Hollywood premiere (all the way back in 2001, if you can
Building to the very top, is this motion a transformation, a
believe it). All the stars are there. So are about a hundred white-
translation, or a rotation?
hot klieg lights. You know, those massive beams that stretch
into the sky for grand openings, major events, and, yes, big
celebs. As they move back and forth, they are bound to form
which of the following?
(A) Angles
(B) Parallel lines
(C) Line segments
(D) All of the above
(A) Rotation
(B) Translation
(C) Transformation and rotation
(D) Transformation and translation
Geometry Unit #1 (geometry basics and transformations)
11) What kind of transformation turns ΔABC into ΔDEF?
12) A community wants to move a skateboard park for safety
and noise reasons. The volunteers decide to move the
skateboard park 128 feet east and 52 feet south. Assuming the
positive y-axis on a coordinate plane as north, which function
represents the translation coordinates of the skateboard park?
(A) (x, y) → (x + 52, y + 128)
(B) (x, y) → (x + 128, y – 52)
(C) (x, y) → (x – 128, y – 52)
(D) (x, y) → (x – 128, y + 52)
(A) Translation
(B) Rotation
(C) Reflection
(D) All of the above
13) The pool of a health club undergoing renovation is being
14) Is it possible for translation, rotation, and reflection to
moved from the center of the bottom floor to the far right roof
produce the same image?
deck. If they want to move the pool up 8 stories and to the right
6 yards, which of the following represents the job the
construction workers need to do?
(A) Yes, this is possible for any image
(B) Yes, this is possible if the original image is in
some way symmetrical
(A) 6 units in the +x direction and 8 units in the
(C) Yes, this is possible only for circular images
+y direction
(D) No, this is never possible
(B) 8 units in the -x direction and 6 units in the
+y direction
(C) 6 units in the -x direction and 8 units in the
+y direction
(D) 8 units in the +x direction and 6 units in the
+y direction
Geometry Unit #1 (geometry basics and transformations)
15) A regular prism has two congruent rectangles as its bases.
16) How many degrees would a regular octagon (the shape of
How can one base be transformed to carry onto the other?
a stop sign) need to be rotated to carry it onto itself?
(A) One base must be rotated to carry onto the other
(A) 20
base
(B) 30°
(B) One base must be reflected to carry onto the other
(C) 45°
base
(D) 60°
(C) One base must be translated to carry onto the
other base
(D) It is impossible to carry one base onto the other
base
17) Chances are you've seen this figure, encouraging you to
18) A trapezoid is a four-sided figure with two sides parallel
"Reduce, reuse, and recycle." Which of the following is true?
to each other. How many axes of symmetry must a trapezoid
have?
(A) 0
(B) 1
(C) 2
(D) 4
(A) Rotation is the only transformation that can carry
the image onto itself
(B) Both rotation and reflection can be used to carry
the image onto itself.
(C) Rotation, reflection, and translation can carry the
image onto itself.
(D) Reflection is the only transformation that can
carry the image onto itself.
19) How many lines of symmetry does a circle have?
(A) 0
(B) 1
20) Look at the angle formed by each spoke stretching to the
outer edge of this wheel. What is the figure's order of
rotational symmetry?
(C) 24
(A) 4
(D) Infinite
(B) 8
(C) 16
(D) Infinity
Geometry Unit #1 (geometry basics and transformations)
21) Which of the following do rigid transformations not do?
(A) Conserve all angles in the figure
22) Which of the following is true about circles and rigid
transformations?
(B) Conserve all lengths in the figure
(A) Translation does not conserve the length of a
(C) Conserve the ability to carry the new figure into
circle's radius.
the original figure
(B) A circle can be carried onto itself regardless of
(D) Rigid transformations do all of the above
any rigid transformation performed on it
(C) Circles are identical after every 1° of rotation
(D) Reflection does not conserve the length of a
circle's radius.
23) Point A has the coordinates (-4, 4). If we want to
24) A triangle has vertices at A (2, 1), B (4, 4), and C (4, 1).
reflect A across the y-axis to make a new point, B, what will the
Another triangle has coordinates at D (7, 3), E (9, 6), and F (9,
coordinates of B be?
3). How many units must ΔABC be translated to carry onto
(A) (4, -4
ΔDEF?
(B) (4, 4)
(A) 5 units to the right, 2 units up
(C) (-4, -4
(B) 5 units to the right, 2 units down
(D) (-8, 8)
(C) 5 units to the right, 5 units up
(D) 2 units up
25) On the x-y plane, ΔABC has coordinates of A (0, 5), B (0,
26) Which two transformation or transformations will create
4), and C (4, 5), while ΔDEF has coordinates of D (-4, 0), E (-4,
trapezoid A'B'C'D' from trapezoid ABCD?
-1), and F (0, 0). How many units must ΔABC be translated to
fit onto ΔDEF?
(A) 4 units down, 2 units to the left
(B) 4 units down, 4 units to the left
(C) 3 units down, 5 units to the left
(D) 5 units down, 4 units to the left
(A) Translation only
(B) Translation and rotation
(C) Translation and reflection
(D) Reflection only
Geometry Unit #1 (geometry basics and transformations)
27) The points of rectangle are L (-4, 6), M (-1, 6), N (-1, 2),
28) The points of rectangle are L (-4, 6), M (-1, 6), N (-1, 2),
and O (-4, 2). The rectangle is first reflected across they-axis
and O (-4, 2). The rectangle is first translated down 4 units
and then translated down 4 units and to the left 1 unit. Which of
and to the left 1 unit and then reflected across the y-axis. Are
the following are the correct coordinates of rectangle L'M'N'O'?
the coordinates of the new rectangle the same as the
(A) L' (3, 2), M' (0, -2), N' (0, 2), O' (3, -2)
coordinates of L'M'N'O' in the previous question?
(B) L' (3, 2), M' (0, 2), N' (0, -2), O' (3, -2)
(A) Yes, because the same transformations are
(C) L' (-5, -10), M' (-2, -10), N' (-2, -6), O' (-5, -2)
performed
(D) L' (-5, -10), M' (0, -10), N' (-2, -2), O' (-5, -6)
(B) No, because different transformations are
performed
(C) No, because the transformations are performed
in a different order
(D) Yes, because all transformations are rigid
29) Which of the following is a rigid transformation?
(A) Dribbling a basketball
(B) Inflating a balloon
(C) Cutting a piece of paper
30) A square mirror has a horizontal scratch in the bottom
right corner. If you reflect the mirror across a horizontal axis
and then rotate it 90° counterclockwise, where will the scratch
be and how will it be oriented?
(D) Opening a laptop
(A) Vertically in the bottom right corner
(B) Horizontally in the top right corner
(C) Vertically in the top left corner
(D) Horizontally in the bottom left corner
31) What is a scale factor?
(A) The number by which the distance from the
32) Which of the following statements is true about the
figure?
center of dilation to an object is multiplied by to
obtain a similar object as measured from the center of
dilation to the dilated object
(B) The number by which the distance from the center
of dilation to an object is subtracted by to obtain a
similar object as measured from the center of dilation
to the dilated object
(C) The coordinate pair of the center of dilation
(D) The distance between the two objects or images
(A) ΔA'B'C' is congruent to ΔABC
(B) ΔABC has been dilated by a factor of 9 to create
the image ΔA'B'C'
(C) ΔA'B'C' has been dilated using O as the center
(D) ΔABC has been dilated using A' as the center.
Geometry Unit #1 (geometry basics and transformations)
33) I can identify and label a point, line and plane.
PROOF OF UNDERSTANDING:
34) I can recognize and explain a dilation in terms of
reduction or enlargement.
PROOF OF UNDERSTANDING:
Point____________
Line ___________
Plane ___________
35) I can identify the various types of transformations in
terms of similar or congruent images.
PROOF OF UNDERSTANDING:
TYPE
TRANSLATION
REFLECTION
ROTATION
SYMMETRY
DILATION
Explain = ___________________________________
36) 1.6 I can correctly name an angle in 3 ways.
PROOF OF UNDERDERSTANDING:
PRODUCES?
similar or conguent
similar or conguent
similar or conguent
similar or conguent
similar or conguent
37) I can construct parallel segments by using slope.
PROOF OF UNDERSTANDING:
__________ __________ __________
38) I can construct perpendicular lines by using slope.
PROOF OF UNDERSTANDING:
Slope of given line = ____________
Slope of given segment = ____________
Geometry Unit #1 (geometry basics and transformations)
39) I can recognize the difference between concave and
convex polygons (also define regular polygon).
PROOF OF UNDERSTANDING:
40) I can bisect an angle using a protractor or paper
folding.
PROOF OF UNDERSTANDING:
________
_________
_______
_________
REGULAR POLYGON =
41) I can construct a perpendicular line by paper folding.
PROOF OF UNDERSTANDING:
42) I can measure and construct an identical angle.
PROOF OF UNDERSTANDING:
_____°
43) I can measure and construct an identical line
segment.
PROOF OF UNDERSTANDING:
44) I can construct a parallel line to a given line through
a point not on the line.
PROOF OF UNDERSTANDING:
Geometry Unit #1 (geometry basics and transformations)
45) I can identify rotational vs. reflectional symmetry.
PROOF OF UNDERSTANDING:
46) I can identify and name a line segment, line, point
and ray.
PROOF OF UNDERSTANDING:
________
________
________
___________
_____________
_____________
________
47) What is the midpoint of the line segment with
endpoints (-9, -7) and (11, 2)?
48) A line segment has one endpoint (-3, -1) and
midpoint (-6, 1). What is its other endpoint?
(A) (-2.5, 1)
(B) (-1, -4.5)
(C) (1, -2.5)
(D) (-4.5, -1)
49) Line segment AB has endpoints (7, 2) and (4, 6).
What are the coordinates of the point that
divides AB in the ratio of 2:3?
(A) (9, -3)
(B) (-4.5, 0)
(C) (-9, 0
(D) (-9, 3)
50) I can recognize the difference between obtuse,
acute, straight and right angles.
PROOF OF UNERSTANDING:
(A) (5.8, 3.6)
(B) (2.2, 1.6)
(C) (5, 4.8)
(D) (-2.6, 1.2)
_______
_______
_______
_________