Name ________________________________________ Date __________________ Class __________________

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25

Congruent Figures Module Quiz: Modified

1. Which best describes the sequence of the transformation given in the graph?

A Rotate ABC 90° clockwise about

the origin and then reflect across the y-axis.

B Reflect ABC over y-axis and then rotate 90° clockwise about the origin.

C Reflect ABC over y-axis and then rotate 90° counterclockwise about the origin.

For 2–3, use the figures below.

ABC XYZ≅

2. What is the side length ?XZ

A Since , .ABC XYZ BC XZ≅ ≅ BC = XZ, and BC = 15 in., so XZ = 15 in.

B Since .ABC XYZ, AC XZ≅ ≅ AC = XZ, and AC = 15 in., so XZ = 15 in.

C Since , .ABC XYZ AC XZ≅ ≅ AC = XZ, and AC = 11 in., so XZ = 11 in.

3. What is the measure of ?C∠ A 31° B 57° C 92°

For 4–5, use the figures below.

ABCD ≅ MNOP 4. Which transformation can be used to map

ABCD to MNOP? A rotation 270° clockwise B reflection across the x-axis C reflection across the y-axis

5. What is the coordinate notation for the transformation used? A (x, y) → (−x, y) B (x, y) → (−x, −y) C (x, y) → (−y, x)

6. Which coordinate notation describes the

transformation in the graph above?

A (x, y) → 1 1,2 2

x y⎛ ⎞⎜ ⎟⎝ ⎠

→ (x − 3, y + 2)

B (x, y) → (2x, 2y) → (x + 3, y − 2)

C (x, y) → 1 1,2 2

x y⎛ ⎞⎜ ⎟⎝ ⎠

→ (x + 3, y − 2)

MODULE

3

Name ________________________________________ Date __________________ Class __________________

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26

Congruent Figures Module Quiz: Modified

For 7–9, use the figures below.

Quadrilateral ABCD ≅ WXYZ

7. What is the length of ?YZ

________________________________________

8. What is the m ?B∠

________________________________________

9a. What is the m ?x∠

________________________________________

9b. Explain your reasoning.

________________________________________

10. KLM is reflected across the y-axis, translated along vector ⟨4, 3⟩, and then dilated which is mapped

(x, y) → 1 1

, .2 2

x y⎛ ⎞⎜ ⎟⎝ ⎠

Graph all of the

transformations.

11. What is the coordinate notation for the transformation shown?

12. RST is the image of NLM under a

series of transformations. Could each of these possible series be used to find the image RST from the preimage

?NLM

a. Reflect RST across y-axis and

then translate along the vector ⟨−2, −4⟩.

____________________________________

b. Reflect RST across x-axis and then rotate counterclockwise 270°.

____________________________________

c. Translate RST along the vector ⟨2, 4⟩, then reflect across the y-axis.

____________________________________

MODULE

3

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118

Lines, Angles, and Triangles Unit Test: B

Use the figure for 1–2.

1. Name all angles congruent to ∠1.

________________________________________

________________________________________

2. Name all angles supplementary to ∠3.

________________________________________

________________________________________

3. Write an equation for the line that passes through (2, −5) and is parallel to 3x + 4y = 8.

________________________________________

4. For the triangles shown, state the additional congruency statement needed to prove BCD QRS≅ for the given theorem.

a. SAS Theorem

____________________________________

b. ASA Theorem

____________________________________

5. Write an equation for the line that passes through (10, 0) and is perpendicular to 3x − y = 7.

________________________________________

For 6–7, use the figure.

6. What is the sum of the interior angles of

this polygon?

________________________________________

7. Using only the sum found above, is it possible to determine the measure of each angle in the figure? Explain why or why not.

________________________________________

________________________________________

For 8–9, use the figure.

8. If m 1 53 ,∠ = ° what is m 3?∠

________________________________________

9. Derrick states that DEF is an isosceles triangle. Is Derrick correct? Explain.

________________________________________

________________________________________

10. Can a triangle have side lengths 5, 8, and 13? Explain why or why not.

________________________________________

UNIT

2

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119

Lines, Angles, and Triangles Unit Test: B

For 11–12, use the figure.

11. If DE = 6x, what is the perimeter of the triangle in terms of x?

________________________________________

12. Can you determine m D∠ with only the information shown? If so, state the measure. If not, explain why not.

________________________________________

________________________________________

________________________________________

13. The sides of a triangle measure 8 meters and 12 meters. What are the possible side lengths for the third side? Show your work.

________________________________________

________________________________________

________________________________________

14. Which points of concurrency must lie inside a triangle? Explain.

________________________________________

________________________________________

________________________________________

For 15–16, use the figure. BCD is shown.

15. Explain how to determine the centroid for

.BCD

________________________________________

________________________________________

16. Where is the centroid for BCD located?

________________________________________

Use the figure for 17–19. Fill in blanks for the paragraph proof.

Given: ∠ ≅ ∠ ,A C BE BD≅

Prove: BA BC≅ 17. It is given that A C∠ ≅ ∠ and .BE BD≅ It

is true that B B∠ ≅ ∠ because

_______________________________________ .

18. Therefore, Δ ≅ ΔBDA BEC by the

_______________________________________ .

19. Thus, BA BC≅ because

_______________________________________ .

UNIT

2

Name ________________________________________ Date __________________ Class __________________

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30

Response to Intervention Post-Test: Congruent Figures

Use the figures for 1–3.

1. List the corresponding angles.

________________________________________

2. List the corresponding sides.

________________________________________

3. Write a congruence statement for the triangles.

________________________________________

For 4–5, use .JKM PQR≅

4. If m∠P = 86° and m∠R = 21°, what is m∠J?

________________________________________

5. If JM = 14 inches and MK = 25 inches, what is the length of RQ?

________________________________________

6. The following congruence statement represents the corresponding parts of two congruent triangles.

BCD RST≅

Choose True or False for each statement.

A BC ST≅ True False

B CB SR≅ True False C C S∠ ≅ ∠ True False D DBC TRS≅ True False

Use the following information for 7–9. The trapezoids below are congruent.

7. What is the length of ?SP

________________________________________

8. Which angle is congruent to ∠B?

________________________________________

9. Which side is longer, QR or RS?

________________________________________

For 10–13, use the figure and the congruence statement .JKM PQR≅

10. What is the measure of ∠Q?

________________________________________

11. What is the measure of ∠M?

________________________________________

12. What is the length of PQ?

________________________________________

13. If the perimeter of triangle PQR is 20 centimeters, what is the perimeter of triangle JKM?

________________________________________

SKILL

7

Name ________________________________________ Date __________________ Class __________________

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36

Response to Intervention Post-Test: Parallelograms

Use the figure for 1–3.

1. List the congruent sides.

________________________________________

2. List the congruent angles.

________________________________________

3. Name two consecutive angle pairs that include ∠C.

________________________________________ Use parallelogram PQRS for 4–5.

4. If m∠P = 2x°, m∠R = 62°, find the value for x.

________________________________________

5. If QR = 16 feet and PS = 3y − 5 feet, find the value for y.

________________________________________

6. Find the unknown angle measures.

________________________________________

7. In parallelogram RSTU, RS || TU and ST || UR . If ST = 9 inches and TU = 4 inches, find RS and UR.

________________________________________

Use parallelogram JKLM for 8–9.

8. What is the value of x?

________________________________________

9. What are the measures of all of the interior angles of the parallelogram?

________________________________________

Use the following information for 10–13. In parallelogram CDEF, AE = 3x + 4, EC = 2x + 8, BE = 4y + 1, and BD = 18.

10. What are the values of x and y?

________________________________________

11. What is the length of ?EC

________________________________________

12. What is the length of ?AC

________________________________________

13. What is the length of ?ED

________________________________________

SKILL

13

Name ________________________________________ Date __________________ Class __________________

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28

Response to Intervention Post-Test: Area of Composite Figures

Use the figure for 1–5.

1. What two shapes make up the figure?

________________________________

2. What is the length of the base of the triangle?

________________________________

3. Find the area of the triangle.

________________________________

4. Find the area of the rectangle.

________________________________

5. What is the total area of the figure?

________________________________

Use the following information for 6–9.

The shaded area represents a square picture frame with a side length of 8 inches. The width of the frame is 2 inches.

6. What is the length of the side of the unshaded square?

________________________________

7. Find the area of the unshaded square.

_________________________________

8. Find the area of the large square.

_________________________________

9. What is the area of the frame represented by the shaded region?

_________________________________

Use the following information for 10–14. Use 3.14 for π. Round answers to the nearest hundredth, if necessary. A window is composed of a rectangle and a semicircle. The height of the window is 7 feet and the width is 4 feet.

10. What is the radius of the semicircle?

_________________________________

11. Find the area of the semicircle.

_________________________________

12. What is the height of the window without the top semicircle?

_________________________________

13. Find the area of the rectangle.

_________________________________

14. What is the total area of the window?

________________________________________

SKILL

5

Name ________________________________________ Date __________________ Class __________________

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32

Response to Intervention Post-Test: Distance and Midpoint Formulas

Use the figure for 1–4.

1. What is the midpoint of AB?

________________________________________

2. What is the midpoint of CD?

________________________________________

3. What is the midpoint of EF?

________________________________________

4. What is the midpoint of GH?

________________________________________

5. A segment has coordinates (−4, 9) and (0, 7). What is the midpoint of the segment?

________________________________________

6. A segment has coordinates (8, −5) and (8, 4). What is the midpoint of the segment?

________________________________________

7. A segment ST is graphed on a coordinate plane. The endpoint S is at (−3, 2). The midpoint is at (−3, −2). What are the coordinates of the other endpoint T?

________________________________________

________________________________________

Use the following information for 8–10. A map is drawn on a coordinate grid.

Each unit is equal to 1 mile.

8. David would like to meet a friend at the halfway point between his home and the library. What is the location of the midpoint between David’s home and the library?

________________________________________

9. What is the distance between the park and the library?

________________________________________

________________________________________

10. What is the distance between David’s home and the park?

________________________________________

________________________________________

11. A segment measures 10 units. One end of the segment has an endpoint at (3, −6). What is another possible endpoint to this segment?

________________________________________

SKILL

9

Name ________________________________________ Date __________________ Class __________________

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44

Response to Intervention Post-Test: Rate of Change and Slope

1. What is the rate of change in the table?

x y

0 0

4 2

8 4

12 6

________________________________________

2. The rate of change for a growing tree is 3 feet every 2 years. What is the unit rate?

________________________________________

Use the graph for 3–6. Calculate the slope for each line.

3. What is the slope of ?AB

________________________________________

4. What is the slope of ?CD

________________________________________

5. What is the slope of ?EF

________________________________________

6. What is the slope of ?GH

________________________________________

7. What is the slope of the line that passes through points (−2, 5) and (6, 10)?

________________________________________

________________________________________

________________________________________

8. What is the slope of the line that passes through points (3, 6) and (−8, 2)?

________________________________________

________________________________________

________________________________________

9. What is the slope of the line that passes through points (9, 0) and (9, −3)?

________________________________________

________________________________________

________________________________________

10. Tell whether each statement is true or false. A Vertical lines have undefined slopes. True False B Slopes must be either positive or

negative. True False C A line with slope −3 goes up from left

to right. True False D If a line has the same y-coordinates,

the slope must be zero. True False

E The slopes 12− and 1

2− are

equivalent. True False

SKILL

21

Name ________________________________________ Date __________________ Class __________________

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49

Response to Intervention Post-Test: Using Slope and y-intercept

For 1–2, use the graph.

1. Find the slope of the line.

________________________________________

2. What is the y-intercept?

________________________________________

3. Write an equation in slope-intercept form for the given slope and y-intercept.

slope: 5; y-intercept: 15

−

________________________________________

4. Find the slope and y-intercept for the graph of the equation y = −x + 4

________________________________________

________________________________________

5. The graph of the following equation has a

slope of 32

. Choose True or False for

each equation.

A y = x + 32

True False

B y = 32

x + 1 True False

C 2x + 3y = 12 True False D −3x + 2y = 4 True False

6. Write the equation 4x + 2y = 6 in slope-intercept form.

________________________________________

7. Find the slope and y-intercept for the graph of the equation −2x + 3y = 1.

________________________________________

________________________________________

8. Graph the equation y = − 34

x + 1.

For 9–10, use the following information.

An amusement park charges $15 per ticket for admission and $5 for parking. The equation y = 15x + 5 represents the total cost y for x tickets. 9. What is the slope of the line? Describe its

meaning.

________________________________________

________________________________________

10. What is the y-intercept? Describe its meaning.

________________________________________

________________________________________

SKILL

26

Name ________________________________________ Date __________________ Class __________________

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51

Response to Intervention Post-Test: Writing Equations of Parallel, Perpendicular, Vertical, and Horizontal Lines

1. State whether the following sets of lines are parallel, perpendicular, or neither. A y = 5 and y = −2

____________________________________

B y = 8 and x = 8

____________________________________

C y = 4x + 8 and y = −4x − 2

____________________________________

D y = −x + 6 and y = x + 1

____________________________________

E y = 6x + 2 and y = 6x

____________________________________

2. What is an equation for the line parallel to y = 2 going through the point (7, −4)?

________________________________________

________________________________________

3. What is an equation for the line parallel to y = 2x + 4 going through the point (1, 1)?

________________________________________

________________________________________

4. What is an equation for the line perpendicular to y = 5x − 1 going through the point (−2, −4)?

________________________________________

________________________________________

5. What is an equation for the line parallel to y = −x + 2 going through the point (−3, −5)?

________________________________________

________________________________________

6. What is an equation for the line perpendicular to x = −1 going through the point (−2, −3)?

________________________________________

________________________________________

7. What is an equation for the line parallel to x = 0 going through the point (6, 5)?

________________________________________

________________________________________

8. What is an equation for the line

perpendicular to 1 13

y x= + going

through the point (−2, 3)?

________________________________________

________________________________________

9. Tell whether each statement is true or false. A Perpendicular lines have opposite

slopes. True False

B The negative reciprocal of 4 is 14

−

True False C Lines that are parallel have the same

slope. True False D Horizontal lines are always

perpendicular. True False E Vertical lines are always parallel. True False F Lines with the same slope are always

parallel. True False G Horizontal and vertical lines are

always perpendicular. True False

SKILL

28