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The School District of Palm Beach County
Department of K-12 Curriculum
Winter Break Student Packet
Geometry
Geometry Secondary Education MAFS.912.G‐CO.1.1 Calculator Neutral for this Standard
Name: _______________________________________________________ Date: ___/___/___ 1. Which student response is the most precise definition of an angle? A. A line that is bent about a center point. B. Two different rays that have a common endpoint. C. Two lines that intersect creating an ‘X’. D. Two non‐parallel lines in different plans that never intersect. 2. Which of the following is a precise definition of perpendicular lines? A. Lines q and p are perpendicular if they never meet. B. Lines q and p are perpendicular if they meet at a single point so that the two lines form a ‘T’. C. Lines q and p are perpendicular if they meet at a single point and if one of the angles at the point of intersection is a right angle. D. Lines q and p are perpendicular if they intersect at the midpoint of q. 3. Which of the following is a precise definition of a circle? A. The set of all points in a plane that are equidistant from a given center point. B. A three‐dimensional shape whose boundary consists of all points equidistant from a given center point. C. The set of all points in a two‐dimensional plane that create a diameter. D. The set of all points that are equidistant to the focus and directrix. 4. Which student response is the most precise definition of a line segment? A. A line segment is part of a line, not the whole thing. B. A line segment is when three points are all on the same line. C. A line segment has an endpoint and continues forever in one direction. D. A line segment is part of a line connecting two endpoints. 5. Which student response is the most precise definition of two parallel lines? A. Two lines are parallel if they are distinct and one can be translated on top of the other. B. Two lines are parallel if they are close together but do not intersect. C. Two lines are parallel as long as they are not perpendicular. D. Two lines are parallel if they do not intersect and are in different planes. Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.1.2 Calculator Neutral for this Standard Name: _______________________________________________________ Date: ___/___/___ 1. Which two transformations map the image in the figure below? Rotation 90 degrees counterclockwise around the origin and a translation. Dilation and a reflection over y = x. Rotation 180 degrees clockwise around the origin and a reflection over the y‐axis. Reflection over the y‐axis and a translation. 2. Which of the following is NOT a rigid motion transformation? A. Translation B. Rotation C. Dilation D. Reflection 3. A city parks and recreation department needs to relocate a swing set so that it is farther away from a new jungle gym that is being installed. The swing set will be reset 48 feet north and 16 feet east of its original position. Assuming the positive y‐axis on a coordinate plane is north, which function represents the translation coordinates of the swing set? A. (x, y) →(x – 16, y – 48) B. (x, y) →(x + 48, y + 16) C. (x, y) →(x + 16, y + 48) D. (x, y) →(x – 48, y – 16) A.
B.
C.
D.
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.1.2 Calculator Neutral for this Standard 4. Draw the image in the graph below for triangle ABC for a translation (x, y) → (x – 5, y + 1), followed by a reflection over the x‐axis. y B A x C 5. Pentagon ABCDE is reflected over the line x = ‐1, followed by a reflection over the line x = 2. Complete the statement below to show the translation of ABCDE to A’’B’’C’’D’’E’’. + – × ÷ 0 2 4 6 8 ( x, y )  ( x
,y
) Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.1.3 Calculator Neutral for this Standard
1. Name: Describe the composition of transformations that will carry the isosceles trapezoid below onto itself. A. reflection over the x‐axis followed by a 180 rotation about the origin B. reflection over the y‐axis followed by a 180 rotation about the origin C. translation according to the rule (x, y) ‐> (x – 2, y + 4) followed by a reflection over the y‐
axis D. rotation of 90 about the origin followed by a reflection over the y‐axis 2. A regular hexagon is rotated on a coordinate plane. Which of the following rotations result in a hexagon with the same appearance as the original? A. 60 clockwise rotation about the center of the hexagon B. 90 clockwise rotation about the center of the hexagon C. 120 clockwise rotation about the center of the hexagon D. 150 clockwise rotation about the center of the hexagon E. 180 clockwise rotation about the center of the hexagon F. 240 clockwise rotation about the center of the hexagon G. 360 clockwise rotation about the center of the hexagon Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.1.3 Calculator Neutral for this Standard
3. A regular polygon has a sides. Which algebraic expression represents the number of degrees of rotation about the polygon’s center that would carry the polygon onto itself? A.
B.
C.
ଵ଼଴
௔
ଷ଺଴
௔
ଷ଺଴
ଶ௔
D. 180(a) 4. Rectangle EFGH is shown on the coordinate plane below. Which sequence of reflections will map EFGH onto itself? A. A reflection over the x‐axis followed by a reflection over the y‐axis B. A reflection over the y‐axis followed by a reflection over the y‐axis C. A reflection over the x‐axis followed by a reflection over the line y = 0.5 D. A reflection over the y‐axis followed by a reflection over the line y = ‐0.5 Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.1.4 Calculator Neutral for this Standard
Name: _______________________________________________________ Date: ___/___/___ 1. A rectangle is translated by the rule ,
interior angle of the new rectangle? →
3,
6 . What will be the measure of each 2. What is the minimum number of degrees that the figure shown below can be rotated so that it maps itself? A. 30° B. 45° C. 60° D. 360° 3. If the image shown below is rotated degrees, will the image be congruent to the preimage? A.
B.
C.
D.
No, parallel lines will result if rotated either 90° or 180°. No, they will become intersecting lines less than 90°. Yes, the rigid motion holds its properties. Yes, but only if rotation either 90° or 180°. Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.1.4 Calculator Neutral for this Standard
4. In the diagram below, ∆
is reflected across the y‐axis to create∆ ′ ′ ′. E E’
D’
D F
F’
Which of the following is true? ∥ ′ ′ A. B. ′ ∥
′ C. ′ ′ D. ′ ′ 5. Which of the following transformations will carry this regular pentagon onto itself? A.
B.
C.
D.
Reflection across m Rotation of 72° clockwise Rotation of 36° counterclockwise Translation , →
2,
2 Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.1.5 Calculator Neutral for this Standard
Name: _______________________________________________________ Date: ___/___/___ 1. Given parallelogram ABCD as shown below, translate ABCD , →
2,
6 and then rotate ABCD 90° counterclockwise about the origin. A B C D 2. Select the combination of transformations that result in the image WXYZ from the pre‐image QRST. Translation Reflection over the x‐axis Reflection over the y‐axis Dilation Rotation 90° counterclockwise Rotation 180° Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.1.5 Calculator Neutral for this Standard
3. Pentagon PENTA was transformed to create the image P’E’N’T’A’. Which of the following describes the transformation shown below? y
P’
E’
A’
P
A
E
N’
T’
x
T
N
A. Reflection over the x‐axis; rotation 180° clockwise about the origin B. Reflection over the y‐axis; rotation 180° counterclockwise about the origin C. Reflection over
; translation , → (x + 0, y – 4) D. Translation , → (x – 1, y + 3) ; reflection over the y‐axis Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.1.5 Calculator Neutral for this Standard
4. Given quadrilateral GHIJ, reflect the figure across the y‐axis and then translate according to the rule , → (x + 7, y + 4). y
H
I
x
G
J
5. Triangle DEF is reflected over the x‐axis and then rotated 90° degrees counterclockwise about the origin. What is the x‐ coordinates of E”? y
E
x
D F
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.2.6 Calculator Neutral for this Standard
Name: _______________________________________________________ Date: ___/___/___ 1. Trapezoid ABCD was transformed to create trapezoid GHEF. Which composition of transformations can be used to show that the trapezoids are congruent? A. A rotation of 90 followed by a translation according to the rule (x, y)  (x – 2, y) B. A translation according to the rule (x, y)  (x, y – 2) followed by a reflection over the y‐axis C. A reflection over the x‐axis followed by a translation according to the rule (x, y)  (x, y – 2) D. A translation according to the rule (x, y)  (x – 2, y) followed by a rotation of 180 2. ∆CDE is located in quadrant I on a coordinate plane. If ∆CDE is reflected across the x‐axis to obtain ∆C’D’E’, which statement is true? A. ∆C’D’E’ lies in quadrant II and is congruent to ∆CDE B. ∆C’D’E’ lies in quadrant II and is not congruent to ∆CDE C. ∆C’D’E’ lies in quadrant IV and is congruent to ∆CDE D. ∆C’D’E’ lies in quadrant IV and is not congruent to ∆CDE Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.2.6 Calculator Neutral for this Standard
3. ∆WXY has vertices W (‐5, 7), X (‐5, 3), and Y(‐2, 3). ∆BCD has vertices B(‐5, ‐6), C (‐5, ‐1), and D (‐2, ‐1). Select the statement that is true. A. The triangles are congruent because ∆WXY can be reflected over the line y = 1 to obtain ∆BCD. B. The triangles are congruent because ∆WXY can be reflected over the line x = 1 to obtain ∆BCD. C. The triangles are congruent because ∆WXY can be translated according to the rule (x, y)  (x, y – 4) to obtain ∆BCD. D. The triangles are not congruent, so ∆WXY cannot be mapped onto ∆BCD 4. Blair draws a triangle on a coordinate plane and performs a series of transformations on it. Select all transformations that will result in an image that is congruent to Blair’s original figure. A. A rotation of 100 followed by a reflection over the x‐axis B. A translation according to the rule (x, y)  (x + 3, y + 6) followed by a dilation with scale factor 5 C. A translation according to the rule (x, y)  (x + 3, y + 6) followed by a translation according to the rule (x, y)  (x – 8, y + 9) D. A reflection over the x‐axis followed by a reflection over the y‐axis E. A translation according to the rule (x, y)  (x + 1, y) followed by a reflection over the line y = x F. A dilation with scale factor 0.3 followed by a rotation of 135 Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.2.7 Calculator Neutral for this Standard
Name: _______________________________________________________ Date: ___/___/___ 1. Scalene triangle EFG is reflected to form ∆MNP. Which statement is true? A.
≅
B.
≅
C. ∠EFG≅∠NMP
D. ∠FGE≅∠NMP
2. The figure below shows ∆ABC and its reflected image, ∆DEF. Describe all of the corresponding parts of the image and pre image that must be congruent. ____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
____________________________________________________________________________
___________________________________________________________________________ Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.2.7 Calculator Neutral for this Standard
3. Guillermo drew ∆RST and then reflected it over line r to create ∆LNE. Guillermo concluded that the triangles are congruent. Which is a correct justification for his conclusion? S N
T R
L
E
r
A. When the triangle was reflected, the angle measures were preserved. B. When the triangle was reflected, the height of the triangle was preserved. C. When the triangle was reflected, the perimeters of the triangle was preserved. D. When the triangle was reflected, the side lengths and angle measures of the triangle were preserved. 4. Triangle ABC has been rotated 180 degrees about the origin to form triangle DBE as shown below. E
B
A D
C Which of the following statements is NOT true. ≅
A.
B. ∠
≅∠
C. ≅
D. ∠
≅∠
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.2.8 Calculator Neutral for this Standard
Name: _______________________________________________________ Date: ___/___/___ 1. Given the information below, can we prove ∆
≅∆
? If yes, which postulate or theorem can be used? D
B 6 cm
22°
C
14 cm
22° E
14 cm A 6 cm
F
A. Yes we can prove the triangles congruent by ASA B. Yes we can prove the triangles congruent by SSS C. Yes we can prove the triangles congruent by SAS D. No, the information is not sufficient to prove the triangles congruent 2. ∆
∆
and ∆PMNare shown below. What additional information is necessary to prove ≅∆
by HL? M
L A.
≅
B. ∠
≅∠
C. ∠
≅∠
D.
 N
P
Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.2.8 Calculator Neutral for this Standard
3. Complete the proof below. H I
Given:
//
,Jisthemidpointof
Prove:∆HIJ≅∆LKJ
J L
K Statements 1.
//
,Jisthemidpointof
Reasons 1. Given
2. ∠IHJ≅∠JLK
2.
3. ∠IJH≅∠KJL
3.
4.
4.
≅
5. ∆HIJ≅∆LKJ
5.
4. ∆ABCanditstranslatedimage∆DEFareshownbelow. What relationship CANNOT be used to prove that ∆ABC is congruent to ∆DEF? A.
B.
C.
D.
Side‐Angle‐Side Angle‐Side‐Angle Side‐Side‐Side Angle‐Angle‐Angle Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.3.9 Calculator Neutral for this Standard
Name: _______________________________________________________ Date: ___/___/___ 1. Savannah is trying to justify to her geometry class that the 2 lines she drew, line a and line b, are parallel. Select all of the reasons that prove Savannah’s lines parallel. a A. 1  3 by the Vertical Angles Theorem b B. 2  8 by the Converse of the Alternate 1 2 4 3 5 6 8 7 Interior Angles Theorem c
C. 1  5 by the Converse of the Corresponding Angles Postulate D. 2  5 by the Converse of the Consecutive Interior Angles Theorem E. by the Converse of the Alternate Exterior Angles Theorem 2. Wellington city engineers are designing two parallel roads by the International Polo Club to help with traffic flow during tournaments. Horse Stables Existing Horse Trail
2 1 Guest Parking 3 4 21° Polo Playing Field The engineers determined that the existing horse trail from the stables to the playing field is 21° south of west to the new road construction as shown in the diagram. Find m4 . Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education Geometry Secondary Education MAFS.912.G‐CO.3.9 Calculator Neutral for this Standard
3. During geometry class, Mr. Jones constructed the perpendicular bisector of segment AB as shown below. A C
B
If AC = 4x + 12 and BC = 2x + 18, find AB. A. 3 C. 24 B. 6 D. 48 4. Which of the following postulates or theorems allows Ms. Snider to prove that two lines are parallel? A. Linear Pair Postulate B. Vertical Angles Theorem C. Converse of the Corresponding Angles Postulate D. Consecutive Interior Angles Theorem 5. In the diagram below, m//n. Select all of the angles that are congruent to ∠1. n
A. ∠2 q p 15 14 13 16 7 6 8 5 3 2 4 1 m
11
10
9
12
B. ∠3 C. ∠5 D. ∠7 E. ∠13 Copyright © 2016 by School Board of Palm Beach County, Department of Secondary Education