Geometry Unit #1 (Geometry Basics and Transformations)

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. / 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.
·  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. / · 
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
*Kaleidoscope Project
*3 Formative Quizzes
*1 Summative Test
1A) I can recognize basic geometric shapes (square, parallelogram, rhombus, diamond, trapezoid, isosceles triangle, pentagon, hexagon, etc.).
PROOF OF UNDERSTANDING:
/ 2A) I can define collinear and coplanar.
PROOF OF UNDERSTANDING:

Collinear = ______
Coplanar = ______
3A) I can identify and name the various parts of a circle (radius, circumference, diameter, arc, etc.).
PROOF OF UNDERSTANDING:

Radius = ______
Diameter = ______
Define circumference = ______
What is an arc? ______/ 4F) I can define the terms congruent and similar.
PROOF OF UNDERSTANDING:
CONGRUENT =
SIMILAR =
Which shapes below are congruent? Which shapes are similar?
5H) I can recognize and understand what proportional shapes look like.
PROOF OF UNDERSTANDING:

What is the value of x? / 6A) I can define the terms finite and infinite.
PROOF OF UNDERSTANDING:
FINITE=
INFINITE=
7A) You are snowboarding down a slope. Which of the following is consistently perpendicular?
(A)Your leg and the board
(B)Your leg and the slope
(C)Your arms, stretched out for balance, and the rest of your body
(D)None of the above / 8A) Which of the following would be considered a true line, in geometric terms?
(A)You, a few friends, and thousands of others standing outside a stadium waiting for tickets to the hottest concert of the year
(B)The direction along which an astronomer is 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
9A) Harry Potter and the Sorcerer's Stone. The night of the big Hollywood premiere (all the way back in 2001, if you can believe it). All the stars are there. So are about a hundred white-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 / 10B) If you ride the elevator from the lobby of the Empire State Building to the very top, is this motion a transformation, a translation, or a rotation?
(A)Rotation
(B)Translation
(C)Transformation and rotation
(D)Transformation and translation
11B) What kind of transformation turns ΔABCinto ΔDEF?

(A)Translation
(B)Rotation
(C)Reflection
(D)All of the above / 12B) 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 positivey-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)
13B) The pool of a health club undergoing renovation is being moved from the center of the bottom floor to the far right roof 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)6 units in the +xdirection and 8 units in the +ydirection
(B)8 units in the -xdirection and 6 units in the +ydirection
(C)6 units in the -xdirection and 8 units in the +ydirection
(D)8 units in the +xdirection and 6 units in the +ydirection / 14B) Is it possible for translation, rotation, and reflection to produce the same image?
(A)Yes, this is possible for any image
(B)Yes, this is possible if the original image is in some way symmetrical
(C)Yes, this is possible only for circular images (D)No, this is never possible
15C) A regular prism has two congruent rectangles as its bases. How can one base be transformed to carry onto the other?
(A)One base must be rotated to carry onto the other base
(B)One base must be reflected to carry onto the other base
(C)One base must be translated to carry onto the other base
(D)It is impossible to carry one base onto the other base / 16C) How many degrees would a regular octagon (the shape of a stop sign) need to be rotated to carry it onto itself?
(A)20
(B)30°
(C)45°
(D)60°
17C) Chances are you've seen this figure, encouraging you to "Reduce, reuse, and recycle." Which of the following is true?

(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. / 18C) A trapezoid is a four-sided figure with two sides parallel to each other. How many axes of symmetry must a trapezoid have?
(A)0
(B)1
(C)2
(D)4
19D) How many lines of symmetry does a circle have?
(A)0
(B)1
(C)24
(D)Infinite / 20D) 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?
(A)4
(B)8
(C)16
(D)Infinity
21F) Which of the following do rigid transformations not do?
(A)Conserve all angles in the figure
(B)Conserve all lengths in the figure
(C)Conserve the ability to carry the new figure into the original figure
(D)Rigid transformations do all of the above / 22F) Which of the following is true about circles and rigid transformations?
(A)Translation does not conserve the length of a circle's radius.
(B)A circle can be carried onto itself regardless of 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.
23F) PointAhas the coordinates (-4, 4). If we want to reflectAacross they-axis to make a new point,B, what will the coordinates ofBbe?
(A)(4, -4
(B)(4, 4)
(C)(-4, -4
(D)(-8, 8) / 24F) A triangle has vertices atA(2, 1),B(4, 4), andC(4, 1). Another triangle has coordinates atD(7, 3),E(9, 6), and F(9, 3). How many units must ΔABCbe translated to carry onto ΔDEF?
(A)5 units to the right, 2 units up
(B)5 units to the right, 2 units down
(C)5 units to the right, 5 units up
D)2 units up
25E) On thex-yplane, ΔABChas coordinates ofA(0, 5),B(0, 4), andC(4, 5), while ΔDEFhas coordinates ofD(-4, 0),E(-4, -1), andF(0, 0). How many units must ΔABCbe 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 / 26E) Which two transformation or transformations will create trapezoidA'B'C'D'from trapezoidABCD?

(A)Translation only
(B)Translation and rotation
(C)Translation and reflection
(D)Reflection only
27F) The points of rectangle areL(-4, 6),M(-1, 6),N(-1, 2), andO(-4, 2). The rectangle is first reflected across they-axis and then translated down 4 units and to the left 1 unit. Which of the following are the correct coordinates of rectangleL'M'N'O'?
(A)L'(3, 2),M'(0, -2),N'(0, 2),O'(3, -2)
(B)L'(3, 2),M'(0, 2),N'(0, -2),O'(3, -2)
(C)L'(-5, -10),M'(-2, -10),N'(-2, -6),O'(-5, -2)
(D)L'(-5, -10),M'(0, -10),N'(-2, -2),O'(-5, -6) / 28F) The points of rectangle areL(-4, 6),M(-1, 6),N(-1, 2), andO(-4, 2). The rectangle is first translated down 4 units and to the left 1 unit and then reflected across they-axis. Are the coordinates of the new rectangle the same as the coordinates ofL'M'N'O'in the previous question?
(A)Yes, because the same transformations are performed
(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
29F) Which of the following is a rigid transformation?
(A)Dribbling a basketball
(B)Inflating a balloon
(C)Cutting a piece of paper
(D)Opening a laptop / 30E) 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?
(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
31H) What is a scale factor?
(A)The number by which the distance from the 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 / 32H) Which of the following statements is true about the figure?

(A)ΔA'B'C'is congruent to ΔABC
(B)ΔABChas been dilated by a factor of 9 to create the image ΔA'B'C'
(C)ΔA'B'C'has been dilated usingOas the center
(D)ΔABChas been dilated usingA'as the center.
33A) I can identify and label a point, line and plane.
PROOF OF UNDERSTANDING:

Point______
Line ______
Plane ______/ 34H) I can recognize and explain a dilation in terms of reduction or enlargement.
PROOF OF UNDERSTANDING:

Explain = ______
35F) I can identify the various types of transformations in terms of similar or congruent images.
PROOF OF UNDERSTANDING:
TYPE / PRODUCES?
TRANSLATION / similar or conguent
REFLECTION / similar or conguent
ROTATION / similar or conguent
SYMMETRY / similar or conguent
DILATION / similar or conguent
/ 36A) 1.6 I can correctly name an angle in 3 ways.
PROOF OF UNDERDERSTANDING:

______
37G) I can construct parallel segments by using slope.
PROOF OF UNDERSTANDING:

Slope of given segment = ______/ 38G) I can construct perpendicular lines by using slope. PROOF OF UNDERSTANDING:
Slope of given line = ______
39A) I can recognize the difference between concave and convex polygons (also define regular polygon).
PROOF OF UNDERSTANDING:

______

______
______
REGULAR POLYGON = / 40G) I can bisect an angle using a protractor or paper folding.
PROOF OF UNDERSTANDING:
41G) I can construct a perpendicular line by paper folding. PROOF OF UNDERSTANDING:
/ 42G) I can measure and construct an identical angle.
PROOF OF UNDERSTANDING:

_____°
43G) I can measure and construct an identical line segment.
PROOF OF UNDERSTANDING:
/ 44G) I can construct a parallel line to a given line through a point not on the line.
PROOF OF UNDERSTANDING:

45E) I can identify rotational vs. reflectional symmetry.
PROOF OF UNDERSTANDING:

______/ 46A) I can identify and name a line segment, line, point and ray.
PROOF OF UNDERSTANDING:

______
______
______
______
47I) What is the midpoint of the line segment with endpoints (-9, -7) and (11, 2)?
(A)(-2.5, 1)
(B)(-1, -4.5)
(C)(1, -2.5)
(D)(-4.5, -1) / 48I) A line segment has one endpoint (-3, -1) and midpoint (-6, 1). What is its other endpoint?
(A)(9, -3)
(B)(-4.5, 0)
(C)(-9, 0
(D)(-9, 3)
49I) Line segmentABhas endpoints (7, 2) and (4, 6). What are the coordinates of the point that dividesABin the ratio of 2:3?
(A)(5.8, 3.6)
(B)(2.2, 1.6)
(C)(5, 4.8)
(D)(-2.6, 1.2) / 50A) I can recognize the difference between obtuse, acute, straight and right angles.
PROOF OF UNERSTANDING: