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2016 Summer Break Packet for Students
Entering Geometry Common Core
ANSWER KEY
PRINCE GEORGE’S COUNTY PUBLIC SCHOOLS
Office of Academic Programs
Department of Curriculum and Instruction
Summer Break Packet
Geometry
In middle school, you worked with a variety of geometric measures, such as
length, area, volume, angle, surface area, and circumference. Rotation,
reflection, and translation were treated with an emphasis on geometric
intuition. In Grade 8, you learned the Pythagorean Theorem and used it to
determine distances in a coordinate system. In high school Geometry, you will
apply these components skills in tandem with others in the course of modeling
tasks and other applications. Therefore, it is important that you keep
practicing your mathematical knowledge over the summer to prepare yourself
for Geometry. In this packet, you will find weekly activities for the Summer
Break. Once you have completed an activity, have a family member sign your
packet. Use a math journal to record and show all your work.
Directions:
 Create a personal and fun Math Journal by stapling several pieces of
paper together or use a notebook or binder with paper. Be creative
and decorate the cover to show math in your world.
 Each journal entry should:
 Have the week number and the activity number.
 Have a clear and complete answer that explains your thinking.
 Be neat and organized.
Playing board and card games are a good way to reinforce basic
computation skills and mathematical reasoning. Try to play board and card
games at least once a week. Some suggested games to play are:
Monopoly, Chess, War, Battleship, Mancala, Dominoes, Phase 10, Yahtzee,
24 Challenge, Sudoku, Connect Four, and Risk.
Don’t forget to bring your journal and signed packet to school on the first
day of school. Your new teacher will be so proud of your summer math
work!
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2016 Geometry Common Summer Packet
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Summer Break Packet
Geometry
Week 1
Domain: Geometry
Standard: 8.G.7 – Apply the Pythagorean Theorem to determine unknown side
lengths in right triangles in real world and mathematical problems in two and
three dimensions.
Directions:
Gloria works at a factory that makes rugs. The edge of each rug is bound with a
braid. Gloria’s Job is to cut the correct length of braid for each rug.
1. The factory makes a rectangular rug that is 4 feet long and 2 feet 6 inches
side. How much braid will Gloria need to go all the way around the rug?
4 feet + 4 feet + 2 feet 6 inches + 2 feet 6 inches =
12 feet + 12 inches =
12 feet + 1 feet =
13 feet
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2016 Geometry Common Summer Packet
Summer Break Packet
Geometry
2. The factory also makes a triangular rug. It is an isosceles triangle 5 feet
wide with a perpendicular height of 1 foot 6 inches. How much braid will
Gloria need to cut to go all the way around the rug?
Base = 60 inches
Height = 18 inches
182 + 302 = c2 = 1224
c ≈ 35
60 inches + 35 inches + 35 inches = 130
Gloria will need about 130 inches of braid to go all the way around the rug.
3. The factory also makes a circular rug that has a diameter of 5 feet. How
much braid will Hank need to go all the way around the circular rug? Give
your answer in whole feet.
diameter = 5
radius = 2.5
C = 2πr
C = πd
C = 5π
C ≈ 15.7 feet
The factory will need about 16 feet of braid to go
all the way around the circular rug.
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Geometry
4. There are plans to make a semi-circular rug, which also has a diameter of 5
feet. Gloria thinks that this rug will need half as much braid as the circular
rug. Explain why Gloria is not correct. How much braid will this rug need?
Sample Response
Gloria is incorrect because although you need half of the braid of the circular
ring, you also need to account for the addition straight side of the semicircular rug. She will actually need half of the 16 feet (8 feet) plus the 5 feet of
the diameter, which means she will need a total of approximately 13 feet of
braid.
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2016 Geometry Common Summer Packet
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Geometry
Week 2
Domain: Geometry
Standard: 8.G.3 – Describe the effect of dilations,
translations, rotations, and reflections on twodimensional figures using coordinates.
Directions:
Andre is drawing some designs for greetings cards. He divides a grid into four
quadrants and starts by drawing a shape in one quadrant. He then reflects,
rotates or translates the shape into the other three quadrants.
1. Finish Andre’s first design by reflecting the shape over the vertical line.
Then, reflect both of the shapes over the horizontal line. This will make a
design in all four quadrants.
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Answer:
2. To finish drawing Andre’s second design, rotate the shape ¼ of a turn in a
clockwise direction about the origin. Then draw the second shape.
Rotate the second shape ¼ of a turn in a clockwise direction about the
origin. Then draw the third shape.
Rotate the third shape ¼ of a turn in a clockwise direction about the origin.
Then draw the fourth shape.
This will make a design in all four quadrants.
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Answer:
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Geometry
3. Below is Andre’s third design. He started with a shape in quadrant IV of the
grid and transformed it to make the design. Describe the transformation
that Andre may have used to draw his design.
Sample Response
He reflects the shape over the vertical line, then translates the 2 shapes up 4
units.
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Geometry
Week 3
Domain: Geometry
Standard: 8.G.7 – Apply the Pythagorean Theorem to
determine unknown side lengths in right triangles in real
world and mathematical problems in two and three
dimensions.
Andros is an ancient city in Russia where some of the
sidewalks are made from small square blocks, 5 cm by 5 cm. The blocks are in
different shades to make patterns. Below is one of the patterns they make. Find
the area and perimeter of the pattern. Show your work. Round to the nearest
whole number.
Perimeter: Length of hypotenuse of small right triangle: 22 + 22 = c2, c = 2.8.
(2 × 8) + (2.8 × 8) = 38.4 ≈ 38.
Area: Area of Triangle = ½ × 4 ×2 = 4. Area of four triangles = 4 × 4 = 16. Area of
square = 8 ×8 = 64. Total area = 64 + 16 = 80.
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Summer Break Packet
Geometry
Week 4
Domain: Geometry
Standard: 7.G.6 – Solve real world and mathematical
problems involving area, volume and surface area of
two- and three-dimensional objects composed of
triangles, quadrilaterals, polygons, cubes, and right
prisms.
Directions: This summer, you are working with a world-famous sports
distributor. They have asked you to design a sports bag they will sell in the fall.
The bag must meet the following criteria.
 The length of the will bag will be 60 cm.
 The bag will have circular ends of diameter 25 cm.
 The main body of the bag will be made of 3 pieces of material (a piece for
the curved body and two circular end pieces).
 Each piece will need to have an extra 2 cm all around it for a seam, so that
the pieces may be stitched.
1. Make a sketch of the pieces you will need to cut out for the body of the
bag. Your sketch does not have to be to scale. On your sketch, show all
the measurements you will need.
10 cm
10 cm
27 cm
62 cm
2. Find the total area of material you will need to create your bag.
(27 × 62) + 2 (π × 102) = 1,674 + 628 = 2,302 cm2
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2016 Geometry Common Summer Packet
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Geometry
Week 5
Domain: Geometry
Standard: 8.G – Use informal arguments to establish facts about the angle sum
and exterior angle of triangles, about the angles created when parallel lines are
cut by a transversal, and the angle-angle criterion for similarity of triangles.
Directions: Use the diagram below to remind you of markings and their
meanings.
These lines are parallel
These lengths are
congruent
These angles are
congruent
1. In the diagram to the below, two 70° angles have been labeled. Four other
angles are labeled w, x, y, and z.
70°
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Complete the table below.
Angle
Determine the measure of the
given angle.
Explain carefully how you
determined the angle measure.
∠ABD ≅ ∠BDC , because when two
parallel lines are cut by a transversal,
alternate-interior angles are congruent.
w
70
∠BAD ≅ ∠x, because when two parallel
lines are cut by a transversal, alternateinterior angles are congruent.
x
70
w + y + 70 = 180 because the sum of
the three angles of a triangle is 180
degrees.
y
40
z + 70 + 70 = 180 because the sum of
the three angles of a triangle is 180
degrees.
z
12
40
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2. The diagram below shows two triangles, triangle ABC and triangle ACD.
Explain how you will determine if the two triangles are similar.
40°
70°
70°
45°
Determine the measures of the unlabeled angles and then verify whether
or not corresponding angles are congruent between the triangles. The
triangles are not similar since corresponding angles are not congruent.
3. The diagram below shows triangle BCD within triangle ACE. Explain
how you will determine if the two triangles are similar.
Determine if congruent angles and proportional sides are corresponding
across the two triangles. The triangles are not similar since
corresponding angles are not congruent.
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Geometry
Week 6
Domain: Geometry
Standard: 7.G – Draw, construct, and describe geometrical figures and describe
the relationship between them.
Directions: A photographer wants to print a photograph and two smaller copies
on the same rectangular sheet of paper. The photograph is 4 inches wide and 6
inches high. The diagrams are not drawn to actual size.
2”
8.5”
3”
3”
3”
Sheet 1
2”
3”
4.5”
Sheet 2
1. Explain how to find the measurements of the small photographs for each
Sheet.
On sheet 1, since the whole length of the photo is 6”, the lengths of the
smaller photos must be 3” each since they are the same size. On sheet 2, the
width of the smaller photos must be 3” each since they are the same size.
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To determine the other measurements, set up proportions using the
corresponding sides and measurements.
Sheet 1:
3
6
𝑥
= ,x=2
4
Sheet 2:
3
4
𝑦
= , y = 4.5
6
2. Find the size of the sheet of paper for each arrangement.
Sheet 1: 6” x 6”
Sheet 2: 8.5” x 6”
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Geometry
Week 7
Domain: Geometry
Standard: 8.G.6-8.G.9 – Understand
and apply Pythagorean Theorem.
Directions: Sean and Kenny are
actors at the local theater. Sean
lives 5 miles from the theater and
Kenny lives 3 miles from the
theater. Their boss wonders how far
apart the actors live from the theater.
 On graph paper, pick a point to represent the location of
the theater.
 Illustrate all of the possible places Sean could live on the graph paper.
 Using a different color, illustrate all of the possible places that Kenny
could live on the grid paper.
1. On your graph paper, label the x and y-axes of the grid. You are going to
plot each scenario on this one grid.
See graphic.
2. Use Pythagorean Theorem, when possible, to compute the distance between
Sean’s and Kenny’s home.
32 + 52 = d2, d = 5.83 miles
3. What is the smallest and largest distance Sean and Kenny live from each
other? How do you know?
The shortest distance is 2 miles; the longest distance is 8 miles.
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4. If Sean lived 5 miles north of the theater and Kenny 3 miles west, what is
the shortest distance between their homes?
32 + 52 = d2, d = 5.83 miles
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Geometry
Geometry – Unit 1 Preview
Standard: G.CO.2 – Represent transformations in the plane using, e.g.,
transparencies and geometry software; describe transformations as functions
that take points in the plane as inputs and give other points as outputs. Compare
transformations that preserve distance and angle measures to those that do not
(e.g., translation versus horizontal stretch).
Part I SAMPLE (Answers will vary.)
1. On a piece of graph paper draw and label a square.
Describe its original position and size.
See graphic.
2. Rotate it 90° clockwise around any point.
See graphic; rotated 90° clockwise about the origin.
3. Translate it so that it is in the 4th quadrant.
See graphic; translated by (-10, 2).
4. Reflect it over a line y = "a number" so that the square is in
the 1st quadrant.
See graphic; reflect over the line y = 5.
5. Write two different ways that you can get the shape back in its original
position.
Rotate 90° counterclockwise and translate by (10, -2).
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Geometry
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Part II SAMPLE (Answers will vary.)
6. On your graph paper, draw and label a
triangle. Describe its original position and size.
See graphic; vertices (7, 5), (11, 5), (7, 12),
base = 4, height = 7.
7. Rotate, translate, and/or reflect the triangle
so that the two triangles create a
parallelogram. List your steps.
Rotate the triangle 180° about point (7, 8.5).
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2016 Geometry Common Summer Packet