staar geometry review reporting category 3

STAAR GEOMETRY REVIEW Reporting Category 3

1

(G.6) Dimensionality and the geometry of location:

The student analyzes the relationship between three-

dimensional figures and related two-dimensional representations and uses these representations

to solve problems.

Name: ____________________________________________________

Date: ____________________________________________________

Period: ____________________________________________________

Topic: (G.6)(A) - Describe and draw the intersection of a given plane with various three-dimensional geometric figures. (Supporting Standard)

Academic Language Notes

Vertex

Prism

Cylinder

Pyramid

Cone

Cube

Cross Section


2

(G.6)(A) Describe and draw the intersection of a given plane with various three-dimensional geometric figures. (Supporting Standard)

1. What shape is the cross section formed by

a cone and a plane that is perpendicular to

the base and that passes through the vertex

of the cone

A. circle

B. triangle

C. trapezoid

D. rectangle

3. Which set of shapes could be cross sections of

a square pyramid?

2. Which of the following best models a

cross section that represents the

intersection of a plane and a prism?

F. A tile on the floor of a room

G. An ice cube from a tray

H. A single card from a deck of cards

J. A bead on a necklace

4. How can a chef cut a cube-shaped cheese to

make slices with triangular faces?

F. Cut the cheese in half from top to bottom

G. Cut the cheese in half from side to side

H. Cut through three edges that meet at one

vertex

J. Cut the cheese diagonally


3

5. Allison has a piece of wood that was in

the shape of a rectangular pyramid. Using

a saw she cut the piece of wood vertically

through the vertex of the pyramid. What

shape is the cross section of the pyramid?

A. triangle

B. rhombus

C. square

D. rectangle

7.

The figure below is intersected by a plane

parallel to its base. What shape is the cross

section?

A. pentagon

B. hexagon

C. square

D. triangle

6. Which of the following shapes cannot

have a cross section in the shape of a

quadrilateral?

F. cylinder

G. pyramid

H. prism

J. sphere

8.

The figure above is intersected by a plane

parallel to the base. What shape could be the

cross-section?

F. circle

G. cone

H. cylinder

J. triangle


4

9. A cylinder-shaped carton of ice cream is cut

by a plane that is perpendicular to the bases.

What is the shape of a cross-section?

A. circle

B. ellipse

C. rectangle

D. triangle

11. How many cross sections shapes can you get

from a sphere?

A. 1

B. 2

C. 3

D. 4

10.

Which of the following shapes could not

represent the cross section of a plane and

pyramid like the one shown?

F. triangle

G. rectangle

H. square

J. trapezoid

12.

Which of the following statements best

describes the intersection of a plane that is

parallel to the base of the pyramid shown

above?

F. The cross section will always be a regular

pyramid.

G. The cross section will sometimes be a

regular pyramid.

H. The cross section will never be a regular

pyramid.

J. Not here


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to solve problems.

Name: ____________________________________________________

Date: ____________________________________________________

Period: ____________________________________________________

Topic: (G.6)(B) - Use nets to represent and construct three-dimensional geometric figures. (Supporting Standard)


Net

Perspective


6

(G.6)(B) Use nets to represent and construct three-dimensional geometric figures. (Supporting Standard)

1. Which net best represents the tetrahedron

shown below?

2. 1) Which of the nets below does not form the

prism pictured?

A. F.

B.

G.

C.

H.

D.

J.


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3. 2) Which net below best represents the solid

figure pictured here?

4. 3) When folded on the dotted lines, which net

will not form a rectangular prism?

4)

F.

5) A.

G.

6)

B.

H.

C.

J.

D.


8

5. Which of the following nets can be

folded along the dashed line to form a

cube??

6. 7) Which net represents a cylinder?

A. F.

B.

G.

C. H.

D.

J.

J)


9




to solve problems.

Name: ____________________________________________________

Date: ____________________________________________________

Period: ____________________________________________________

Topic: (G.6)(C) - Use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems. (Supporting Standard)


2-Dimensional Figure

3-Dimensional Figure

Perspective

Orthographic View

Isometric View

Surface Area

Volume


10

(G.6)(C) Use orthographic and isometric views of three-dimensional geometric figures to represent and construct three-dimensional geometric figures and solve problems. (Supporting Standard)

1. 1) The three-dimensional figure below is

constructed from 16 identical blocks.

Which of the following best represents the

same structure from a different view?

2. 2) The top and front side view of a three-

dimensional structure are shown below.

Top Front

Which structure corresponds with these

images?

A.

F.

B.

G.

C.

H.

D.

J.


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3. 8) Which diagram shows the top view of the

solid below?

9)

4.

Which is the correct isometric drawing of the

figure with the orthographic drawing shown

above?

A.

F.

B.

G.

C.

H.

D.

J.


12

5. 3) What is the volume of a 3-dimensional object with the dimensions shown in the three views below?

Record your answer and fill in the bubbles on grid.


13

(G.7) Dimensionality and the

geometry of location: The student understands that

coordinate systems provide convenient and efficient ways

of representing geometric figures and uses them

accordingly.

Name: ____________________________________________________

Date: ____________________________________________________

Period: ____________________________________________________

Topic: (G.7)(A) - Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures. (Supporting Standard)


1-Dimensional Coordinate System

2-Dimensional Coordinate System

Points

Lines

Rays

Line Segments

Figures


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(G.7)(A) Use one- and two-dimensional coordinate systems to represent points, lines, rays, line segments, and figures. (Supporting Standard)

1. The graph for GK below maps one fourth of the course for 10km marathon. Water and first aid

stations are placed throughout the course as shown.

Using the clues below, how many more meters would a participant at Water Station H need to run to

reach First Aid Station I?

I. The distance from Start to Water Station H is 510 m.

II. The distance from Start to Water Station J is 1.94 km.

III. The distance from Water Station H to First Aid Station I is 30 meters less than the distance from

First Aid Station I to Water Station J.

A. 560 m B. 625 m C. 700 m D. 730 m

2.

On Main Street, the post office is the midpoint between the restaurant and the parking garage. The

public restroom is the midpoint between the restaurant and the post office, and the public phones are

located midway between the public restrooms and the parking garage.

If the distance from the restrooms to the post office is 12 yards, how far is it from the restaurant to

the public phones?

F. 18 yards G. 24 yards H. 30 yards J. 36 yards

Water

H

Start

G

1st Aid

I

Water

J

1st Aid

K

A B C D E.


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3. Which of the following best describes the

graph of the inequality -5 ≤ x ≤ 1?

A. point

B. line

C. ray

D. segment

6. Which of the following relationships could

not be used to determine the length of DR, as

shown below?

F. DF + FQ + QR = DR

G. DQ + QR = DR

H. DQ + FR = DR

J. DF + FR = DR

4. Which of the following inequalities when

graphed would best represent opposite rays?

F. x < 4 and x > 4

G. x ≤ 4 and x > 4

H. x < 4 and x ≥ 4

J. x ≤ 4 and x ≥ 4

7.

If the circle shown has a radius of 4 units,

which of the following points would not be on

the circumference of the circle?

A. (6, -3)

B. (-2, 6)

C. (2, 1)

D. (-2, -3)

5. If a circle has as its center the point (-3, -4)

and a radius of 4.5 units, through which

quadrant(s) does the circle pass?

A. II, III, and IV

B. 1, III, and IV only

C. 1, II, and IV only

D. III, and IV only


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8. A hexagon is graphed on the coordinate grid.

Which two coordinate points lie on the same

line of symmetry on this hexagon?

F. (–3, –1) and (0, 3)

G. (–1, 3) and (–1, –1)

H . (0, 3) and (0, –1)

J. (–4, 1) and (1, 1)

9.

Four students are choreographing their

dance routine on a stage that measures 15

yards by 10 yards. Three of the students -

Rebecca (R), Krista (K) and Julian (J) -

graphed their starting positions as shown on

the grid on the right. If the fourth student,

Enrique (E) is no more than 4 yards away

from any of the other three students, which

coordinate could represent his starting

position?

A. (8, 8)

B. (8, 5)

C. (9, 3)

D. (10, 4)

10.

Parallelogram ABCD is graphed on the

coordinate plane shown below. What are the

coordinates of point C?

F. (x, y)

G. (y, x + z)

H. (x + z, y)

J. (x - z, y)

y


17





accordingly.

Name: ____________________________________________________

Date: ____________________________________________________

Period: ____________________________________________________

Topic: (G.7)(B) Use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons (READINESS STANDARD)


Slope

Slope-Intercept form of a linear equation

Standard form of a linear equation

Parallel lines

Perpendicular lines

Opposite reciprocal


18

(G.7)(B) Use slopes and equations of lines to investigate geometric relationships, including parallel lines, perpendicular lines, and special segments of triangles and other polygons (READINESS STANDARD)

1. Given P(3, 7), Q (-2, -8), R(0, 3) and S(-4, -9),

what is the relationship between and

?

A. The lines are parallel.

B. The lines are perpendicular.

C. The points are collinear.

D. The lines are skew.

3. The rays graphed below represent varying rates of

change, or speed, from the relationship

. Which ray represents a slope, or

rate of change that is closest to 45 mph?

A.

B.

C.

D.

2. Which of the following best describes the

graph of the system of equations shown

below?

6x − 14y = −28

3y − 7x = −14

F. The lines are parallel.

G. The lines are the same.

H. The lines intersect but are not

perpendicular.

J. The lines intersect and are perpendicular.


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4. A right triangle is formed by the x-axis, the

y-axis and the line , as shown

below.

Which pair of equations can be used to

create a fourth vertex such that a rectangle is

formed?

F. and

G. and

H. and

J. and

5. Which equation describes the graph of a line

perpendicular to the one shown on the graph?

A.

B.

C.

D.


20

6.

Points W, X, Y and Z represent the vertices

of a parallelogram. Which of the following

equations does not represent the equation of

a line that contains one of the sides of the

parallelogram?

F. y = -3

5x +

3

8

G. 5x + 3y = 8

H. y = -3

5x + 16

J. 5x + 3y = 16

7.

Which of the following equations does not

represent the perpendicular bisector of one of

the sides of the triangle?

F. y = 3

G. x = 3

H. y = -x + 9

J. y = x – 3

8.

Which of the following best describes at least one step

to prove whether or not parallelogram ABCD is a

rectangle?

A. Determine if slopes of AD and AB are equal.

B. Determine if slopes of AD and AB are opposite

reciprcals.

C. Determine if the slopes of AD and BC are

reciprocals.

D. Determine if the slopes of AD and BC are opposite

reciprocals


21





accordingly.

Name: ____________________________________________________

Date: ____________________________________________________

Period: ____________________________________________________

Topic: (G.7)(C) [Derive and] use formulas involving length, slope, and midpoint. (READINESS STANDARD)


Slope Formula

Midpoint

Midpoint Formula

Length

Distance Formula


22

(G.7)(C) [Derive and ] use formulas involving length, slope, and midpoint. (READINESS STANDARD)

1. In a baseball diamond, or rhombus, all of the

angles measure also making it a square. If

the bases are graphed as shown below, to the

nearest tenth, what is the direct distance

between home plate (shown at the origin) and

second base?

A. 63.8 ft.

B. 127.3 ft

C. 153.7 ft

D. 180 ft

2.

Of the segments graphed below, which one is

the closest to having a length of 5 units?

F.

G.

H.

J.

3.

Which of the following segments has a midpoint

located at -4?

A. PQ

B. PR

C. PS

D. PT

A

B

C

D

E.

F

G

H

2 4–2–4 x

2

4

–2

–4

y


23

4. On the hexagon graphed below, what is the

slope of the line of symmetry that bisects

and ?

F.

G.

H.

J.

5.

A coordinate grid is placed over a map. City A is

located at (–3, 2), and City B is located at (4, 8).

If City C is at the midpoint between City A and

City B, which is closest to the distance in

coordinate units from City A to City C?

A. 4.61 units

B. 6.52 units

C. 9.22 units

D. 21.25 units

6.

AB is a diameter of the circle shown below.

Which is closest to the length of the radius of the

circle?

F. 3.1 units

G. 4.3 units

H. 6.1 units

J. 12.2 units

F

G H

I

JK2 4 6 8 10 x

2

4

6

8

10

y

y

x0 1 2 3 4 5 6 7 8

1

2

3

4

56

7

8

-1

-2

-3-4-5-6-7-8 -1-2

-3

-4

-5

-6-7

-8

9

9

y


24

7. A line segment has an endpoint at (3, 2).

If the midpoint of the line segment is

(6, -2), what are the coordinates of the

point at the other end of the line segment?

A. (4.5 , 0)

B. (0 , 6)

C. (9 , 4)

D. (9 , -6)

9. ΔABC has vertices at A(0, 0), B(9, 12), and

C(25, 0). What is the distance between the

midpoint of AB and the midpoint of AC ?

A. 7.5 units

B. 10 units

C. 15 units

D. 20 units

8. If ABCD is a parallelogram, what are the

coordinates of point B?

F. (3, 7)

G. (5, 5)

H. (7, 8)

J. (7, 3)

10. What is the distance between the points

(-3, 5) and (5, -1)? Round to the nearest

hundredth of a unit as necessary.

Record your answer and fill in the bubbles on

grid.

staar geometry review reporting category 3

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