Download Reporting Category 2

STAAR GEOMETRY REVIEW
Reporting Category 2
Name: ____________________________________________________
(G.4) Geometric structure:
The student uses a variety of
representations to describe
geometric relationships and
solve problems.
Date:
____________________________________________________
Period: ____________________________________________________
Topic:
(G.4)(A) - Select an appropriate representation ([concrete,]
pictorial, graphical, verbal, or symbolic) in order to solve
problems. (Supporting Standard)
Academic Language
Notes
Concrete Representation
Pictorial Representation
Graphical Representation
Verbal Representation
Symbolic Representation
Geometric Patterns
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STAAR GEOMETRY REVIEW
(G.4)(A)
1.
Reporting Category 2
Select an appropriate representation ([concrete,] pictorial, graphical, verbal, or
symbolic) in order to solve problems. (Supporting Standard)
2.
Which of the following does not necessarily
represent line l parallel to line m and
intersected by line t?
A circular pizza is cut into 12 equal pieces.
The tip of each piece forms what angle?
F. 20º
G. 25o
A.
H. 30o
J. 35o
3.
B.
Look at the figure shown below.
C.
Which expression does not represent the area
of the figure?
A. bc − ef
D.
B. af + ad − de
C. de + af + ad
D. af + cd
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STAAR GEOMETRY REVIEW
4.
Reporting Category 2
6.
If angle A and angle B are supplementary
angles and the measure of angle A is x,
which equation can be used to find y, the
measure of angle B?
Find the equation that can be used to
determine the total area of the composite
figure shown below.
F. y = 90 + x
G. y = 90 – x
H. y = 180 – x
1
2
J. y = x + 180
A. A  lw  w 2
B. A  lw  w 2
C. A  w  2l  w 2
1
2
D. w  2l  w 2
5.
7.
A regular hexagon is broken into the 6
triangles as shown below. What are
the measurements of the interior
angles of ABC ?
C
A
New York Time
12:00 NOON
California Time
9:00 A.M.
Eastern time
Pacific Time
At which of the following times of day will
the hour and minute hands of a clock in New
York form an angle that is complementary to
the angle formed by the hands of a clock in
California.
B
A. 30o, 60o, 90o
F.
1:00 P.M.
B. 40o, 60o, 90o
G.
3:00 P.M.
C. 60o, 60o, 60o
H.
8:00 P.M.
D. 30o, 60o, 60o
J.
10:00 P.M.
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STAAR GEOMETRY REVIEW
8.
Reporting Category 2
10. In the figure shown below, BC is parallel to
Look at the cube shown below.
ED , and AE is perpendicular to ED . The
measure of  ABC is 130°.
s
Which equation best represents the area of
the shaded rectangle located diagonally in
the cube?
A. s 2 3
B.
9.
s3
2
C. s
3
D. s
2
What is the measure of angle BAE in degrees?
Record your answer and fill in the bubbles on
2
grid.
2
Dolores had a circular garden with a
radius of 30 feet. She used all of the
fencing from the circular garden to
enclose a square garden. The length of
each side of Dolores’s square garden
was approximately:
F. 47 feet
G. 94 feet
H. 120 feet
J. 188 feet
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STAAR GEOMETRY REVIEW
Reporting Category 2
Name: ____________________________________________________
(G.5) Geometric pattern:
The student uses a variety of
representations to describe
geometric relationships and
solve problems
Date:
____________________________________________________
Period: ____________________________________________________
Topic: (G.5)(A) - Use numeric and geometric patterns to develop
algebraic expressions representing geometric properties.
(READINESS STANDARD)
Academic Language
Notes
Patterns
Numeric Patterns
Geometric Patterns
Algebraic Expressions
Geometric Properties
5
STAAR GEOMETRY REVIEW
Use numeric and geometric patterns to develop algebraic expressions representing
geometric properties. (READINESS STANDARD)
(G.5)(A)
1.
Reporting Category 2
The figure at the right shows a conical cup
containing water. The water depth can be
represented by x, and the area of the water
surface can be represented by A. As the water
depth changes, the area of the water surface
changes, as shown in the table below.
Which equation best represents the
relationship between the area of the water
surface and the water depth?
A. A 
 2 x  12
16
B. A 
C. A 
D. A 
2.
x
2
x 2
16
x
16
in 2
in 2
in 2
in 2
The figure shows the first 3 stages of a fractal.
Which expression describes the number of
shaded squares in the nth figure of the pattern?
F. 3n  1
G. 3 n 1
H. 3 n  1
J. Not here
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STAAR GEOMETRY REVIEW
3.
Reporting Category 2
Use the table to determine the expression
that best represents the number of diagonals
of any convex polygon having n sides.
Polygon
Number
of Sides
Number of
Diagonals
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
3
4
5
6
7
8
0
2
5
9
14
20
5.
Ms. Morales asked her students to write an
equation to represent the number of white tiles,
t, for any figure number, n.
Which equation represents the number of white
tiles in the pattern?
A.
t=n+2
A. n  3
B.
t=n+4
n3
2
C.
t = 4n + 4
B.
D.
t = 4n + 8
C.
nn  3
2
D. nn  3
4.
The figure below shows the first 3 stages of a
fractal.
6.
The first 4 stages of a geometric pattern are
shown below.
How many circles will the nth stage of this
fractal contain?
If each square represents 1 square unit, which
expression can be used to determine the
number of square units at stage n?
F. 2n
F. n  12  3
G. 2 n
G. 2n  1
H. 2n  1
H.
J. 2  1
n
n
n  1
2
J. 3n  1 =
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STAAR GEOMETRY REVIEW
7.
8.
Reporting Category 2
A nesting of squares is created by starting
with a square, then inscribing a square
rotated by 45o within, and then repeating the
process as shown in the figure for 3 squares.
If n squares are so nested, into how many
regions is the original square divided?
A.
4n - 4
B.
4n - 3
C.
4n
D.
4n + 1
A townhouse builder used arrangements of
toothpicks to describe his latest plan to a
coworker. The diagram below show the
toothpick arrangement he used for 1 and 2
townhouses.
Which expression can be used to determine
the number of toothpicks the builder will
need to represent y connected houses?
F. 6y
G. 6y-1
H. 5y
J. 5y+1
9.
Cristian uses tiles to create a rectangle with
an area of 32 square inches. Let n represent
the number of rectangles in the pattern.
Which expression can be used to find the
area of a pattern with n rectangles?
A. 32n
B. n + 46
C. 9n + 23
D. 4(9n) – 2
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STAAR GEOMETRY REVIEW
Reporting Category 2
Name: ____________________________________________________
(G.5) Geometric pattern:
The student uses a variety of
representations to describe
geometric relationships and
solve problems
Date:
____________________________________________________
Period: ____________________________________________________
Topic: (G.5)(B) - Use numeric and geometric patterns to make
generalizations about geometric properties, including properties
of polygons, ratios in similar figures and solids, and angle
relationships in polygons and circles. (Supporting Standard)
Academic Language
Notes
Numeric Patterns
Geometric Patterns
Geometric Properties
Polygons
Ratio
Solids
Angle Relationships
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STAAR GEOMETRY REVIEW
(G.5)(B)
1.
Reporting Category 2
Use numeric and geometric patterns to make generalizations about geometric
properties, including properties of polygons, ratios in similar figures and solids, and
angle relationships in polygons and circles. (Supporting Standard)
Which expression shows the number of
vertices in a pyramid whose base is an
n-sided polygon?
3.
Which of the following measures could not be
the 3 sides of a triangle?
A. 21, 28, and 35
A. n
B. 8, 9, and 17
B. n + 1
C. 2.5, 3, and 5
C. 2n
D. 2, 3.5, 4
D. 2n + 1
2.
If a circle were divided into 4, 6, or 9 equal
sectors, which of the following shows their
respective measures of the central angles of
the sectors?
4.
Jose made a fence around his garden. Each
vertex had an exterior angle measurement of
40o. The fence formed a regular polygon.
Which is the shape of the fence?
F. 90°, 60°, 40°
F. Hexagon
G. 45°, 30°, 20°
G. Heptagon
H. 90°, 60°, 45°
H. Octagon
J. 180°, 90°, 60°
J. Nonagon
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STAAR GEOMETRY REVIEW
5.
Reporting Category 2
∆JKE is an obtuse isosceles triangle with
m  E = 10o and KE>JK. What is m  J?
7.
A. 170o
B. 160o
C. 85o
Felicia notices that in an equilateral triangle,
each interior angle measures 60o and in a
square, each interior angle measures 90o.
Which of the following expressions could be
used to determine the measure of each interior
angle of a regular polygon with n sides?
A. (n  2) *180
D. 10o
B.
(n  2) *180
n
C. (n  2) * 360
D.
6.
Shown below is ABC . What is the sum
of the ABC and BCA ?
8.
125o
(n  2) * 360
n
A square is attached to one side of a regular
hexagon and matches up exactly. The square
has a side length of 4 centimeters. Find the
perimeter of the new composite polygon and
classify the new polygon.
F. 32 centimeters; octagon
G. 32 centimeters; nonagon
H. 40 centimeters; decagon
F. 65o
J. 40 centimeters; nonagon
G. 75o
H. 90o
J. 125o
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STAAR GEOMETRY REVIEW
9.
Reporting Category 2
On the map below, First Avenue and Second
Avenue are parallel. A city planner proposes
to locate a small garden and park on the
triangular island by the intersections of four
streets shown.
A. 90°, 65°, 25°
B. 90°, 50°, 40°
C. 90°, 60°, 30°
D. 130°, 40°, 10°
10.
A portion of a regular polygon is shown.
How many sides does the polygon have?
F. 15 sides
G. 16 sides
H. 18 sides
J. 20 sides
11.
What is the measure of each interior angle in
a regular dodecagon?
Record your answer and fill in the bubbles
on your answer document.
12
STAAR GEOMETRY REVIEW
Reporting Category 2
Name: ____________________________________________________
(G.5) Geometric pattern:
The student uses a variety of
representations to describe
geometric relationships and
solve problems
Date:
____________________________________________________
Period: ____________________________________________________
Topic:
(G.5)(C) - Use properties of transformations and their
compositions to make connections between mathematics and the
real world, such as tessellations. (Supporting Standard)
Academic Language
Notes
Transformations
Translations
Rotations
Reflections
Dilations
Tessellations
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STAAR GEOMETRY REVIEW
(G.5)(C)
1.
Reporting Category 2
Use properties of transformations and their compositions to make connections between
mathematics and the real world, such as tessellations. (Supporting Standard)
The first 4 stages of a certain fractal are shown below.
In each stage after the first, each square is divided into 4 squares, and then the bottom right square is
removed. If the pattern continues, how many shaded square units will Stage 5 contain?
A. 243
B. 54
C. 81
D. 27
2.
Which sentence better describes a
tessellation?
3.
F. A tiling where a shape is repeated
through a plane without any gaps
or overlaps.
Which of the polygons listed below can be
used to create a tessellation by itself?
A. Regular Octagon
B. Regular Nonagon
C. Regular Decagon
G. A tiling created exclusively by
triangles and trapezoids.
D. None of the above.
H. A pattern showing the translation
of a square.
J. None of the above.
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STAAR GEOMETRY REVIEW
4.
Which shape was used to create the
following tessellation?
Reporting Category 2
5.
Look at the figure below
Which of these patterns can be made using
only translations, rotations, or a combination of
translations and rotations?
I.
F.
II.
G.
III.
H.
A. I and II only
B. I and III only
J.
C. II and III only
D. I, II and III
6.
∆A’B’C’ is the image if ∆ABC under what
type of transformation?
F. reflection
G. rotation
H. translation
J. dilation
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STAAR GEOMETRY REVIEW
7.
Which shape could not be use alone to from a tessellation?
A.
8.
Reporting Category 2
B.
C.
D.
The figure graphed below is rotated 90o clockwise about the origin and translated up 1 unit.
Which is the resulting image?
F.
G.
H.
J.
16
STAAR GEOMETRY REVIEW
Reporting Category 2
Name: ____________________________________________________
(G.5) Geometric pattern:
The student uses a variety of
representations to describe
geometric relationships and
solve problems
Date:
____________________________________________________
Period: ____________________________________________________
Topic: (G.5)(D) - Identify and apply patterns from right triangles to
solve meaningful problems, including special right triangles
(45 o-45 o-90 o and 30 o-6 0 o-90 o) and triangles whose sides are
Pythagorean triples. (READINESS STANDARD)
Academic Language
Notes
Right Triangles
Special Right Triangles
45o-45o-90o Triangle
30o-60o-90o Triangle
Pythagorean Theorem
Pythagorean Triple
17
STAAR GEOMETRY REVIEW
(G.5)(D)
1.
Reporting Category 2
Identify and apply patterns from right triangles to solve meaningful problems,
including special right triangles (45o-45 o-90 o and 30 o-60 o-90 o) and triangles whose
sides are Pythagorean triples. (READINESS STANDARD)
ΔKMS has a right angle at M. The measure
of  MSK = 60°, and KS = 17 centimeters.
Which is closest to the length of KM?
3.
What are the values of x and y in the figure
below?
A. 9 cm
B. 12 cm
C. 10 cm
D. 15 cm
A. x = 12, y = 6 2
B. x = 12, y = 6 3
C. x = 6 2 , y = 6
D. x = 6 3 , y = 12
2.
Megan is using an equilateral triangle as
part of a design on a sweatshirt. Each side
of the triangle is 12 inches long. Megan is
sewing a line of sequins from the midpoint
of one side of this triangle to the opposite
vertex. Approximately how long will the
line of sequins be?
4.
A fence around a square garden has a
perimeter of 48 feet. Find the approximate
length of the diagonal of this square garden.
F. 12 feet
G. 17 feet
H. 21 feet
J. 24 feet
F. 13.4 in.
G. 10.4 in.
H. 8.5 in.
J. 5.2 in.
18
STAAR GEOMETRY REVIEW
5.
Reporting Category 2
Mr. Ryan is flying his single-engine plane at
an altitude of 2400 feet. He sees a cornfield
at an angle of depression of 30°.What is Mr.
Ryan’s approximate horizontal distance from
the cornfield at this point?
A. 1200 feet
B. 3394 feet
C. 4157 feet
D. 4800 feet
6.
A kite string is 220 feet long from the kite to
the ground. The string makes a 45° angle
with the ground. About how high off the
ground is kite?
F. 110 ft
G. 127 ft
H. 156 ft
J. 311 ft
7.
Mr. Schultz has a garden shaped like an
equilateral triangle that measures 11 feet on
each side. He has placed a watering hose that
extends from the faucet located at a vertex to
the opposite side, as shown below. Which is
closest to the length of the hose in the
garden?
A. 7.8 ft
B. 9.5 ft
C. 6.4 ft
D. 5.5 ft
19
STAAR GEOMETRY REVIEW
8.
In the figure shown below, MN = 10
centimeters.
Reporting Category 2
9.
The lengths of the bases of an isosceles
trapezoid are shown below.
14 units
8 units
If the perimeter of this trapezoid is 32 units,
what is its area?
A. 44 square units
B. 110 square units
C. 88 square units
D. 55 square units
Which is closest to the length of TN ?
F. 7 cm
G. 6 cm
H. 17 cm
J. 14 cm
10.
In ∆XYZ, what is approximate the length of
XY . Round your answer to the nearest
hundredth of an inch. Record your answer
and fill in the bubbles on grid
20