Chapter Test x 7 Form A continued Chapter TestSimilarity Form A …caronnaclassroom.weebly.com/uploads/1/3/3/8/13388109/... · 2019. 8. 24. · 46 feet long, and 14 feet wide. The

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39. A 10 ft. long ladder is leaning against a tall office building, 6 ft. above the ground. The ladder is moved closer to the building, such that the horizontal distance travelled is 3 times the vertical distance covered by the ladder. Find how far is the ladder from the building now?

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. 42.

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Name ________________________________________ Date ___________________ Class __________________

Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

Holt McDougal Geometry

Similarity Chapter Test Form A

1. Determine whether the triangles are similar. If so, write the similarity ratio and a similarity statement.

_________________________________________

2. A rectangular field has a length of 105 feet and a width of 60 feet. On a map of the field, the width was drawn as 4 inches. What measurement should represent the length?

_________________________________________

3. A portion of a daycare has been set aside for toddlers under 2. The dimensions are shown. A scale drawing of the room is 5 cm tall. How wide is the scale drawing?

_________________________________________

4. Give the definition of a dilation.

_________________________________________

5. Apply the dilation D: (x, y) ĺ (3x, 3y) to the polygon A(4, 4), B(1, 1), C(6, 8). What are the coordinates of the image points?

_________________________________________

6. Name the dilation and then the translation that was used to map O(2, 5), P(6,1), Q(0, –1), R(–1, 0) to A(8, 14), B(16, 6), C(4, 2), D(2, 4).

________________________________________

________________________________________

7. Identify the similarity postulate or theorem that can be used to prove

ABE CDE.

________________________________________

8. Find DF.

________________________________________

9. Write True or False. ||MN KL

________________________________________

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Similarity Chapter Test Form B

1. Determine whether ABC and DEF are similar. If so, write the similarity ratio and a similarity statement.

_________________________________________

2. Jamestown, North Dakota, claims to have the world s largest bison (American buffalo) statue. The statue is 26 feet high, 46 feet long, and 14 feet wide. The statue is similar to an actual bison that is 6 feet tall. About how long is the actual bison to the nearest foot?

_________________________________________

3. The scale drawing of a triangular swimming pool has the dimensions shown. The longest side of the actual swimming pool is 8 m. What is the length of the actual swimming pool?

_________________________________________

4. Give an example of a transformation that is NOT a similarity transformation.

_________________________________________

5. Describe the dilation

D: (x, y) ĺ § ·¨ ¸© ¹

4 4, .5 5

x y

________________________________________

________________________________________

6. Tell how polygon A(0, 0), B(5, 4), C(3, 2), D(–1, –1) was mapped to polygon E(2, 2.5), F(4.5, 4.5), G(3.5, 3.5), H(1.5, 2).

________________________________________

________________________________________

7. Explain why the triangles are similar and write a similarity statement.

________________________________________

________________________________________

________________________________________

________________________________________

8. Find SP.

________________________________________

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form A continued

10. Find RQ.

_________________________________________

11. Mentone, Indiana, claims to have the world's largest egg sculpture. A 6-foot-tall person standing next to the egg sculpture casts a shadow that is 2 feet long. If the egg casts a shadow that is 4 feet long, how tall is the sculpture?

_________________________________________

12. A drawing of a garden uses a scale of 1 in : 3 ft. Find the length of the garden if the length on the drawing is 13 inches.

_________________________________________

13. Given that UOV is a dilation image of SOT, find the coordinates of V and the

scale factor.

________________________________________

14. Given: A(0, 0), B(0, 3), C(4, 0), D(0, 6), and E(8, 0) Prove: ABC ADE

________________________________________

________________________________________

________________________________________

________________________________________

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Circle the best answer. 1. Which similarity statement is true for

rectangles JKLM and PQRS, given that JK 6, JM 5, QR 15, and PQ 12.5?

A rectangle JKLM rectangle PQRS B rectangle JKLM rectangle QRSP C rectangle JKLM rectangle RQPS D rectangle JKLM rectangle SRQP

2. JKL MNO. The similarity ratio of

JKL to MNO is 52

. What is the length

of MN ?

F 6 G 10.8 H 14 J 37.5

3. An atrium has the dimensions shown. A scale drawing of the atrium is actually 6 cm wide. What is the length of the scale drawing?

A 1.9 cm C 19.2 cm B 3.3 cm D 48 cm

4. Which of the following transformations is NOT a similarity transformation? F M: (x, y) (0.3x, 0.3y) G M: (x, y) (10x, 10y) H M: (x, y) (4x, 2y) J M: (x, y) (0.8x, 0.8y)

5. The dilation D: (x, y) § ·¨ ¸© ¹

3 3, 4 4

x y has

been applied to the polygon S(12, 16), T(–12, –16), U(4, 4). What are the coordinates of the image points? A S'(9, 12), T'( 9 , 12), U'(3, 3) B S'(36, 48), T'( 36, 48), U'(12, 12) C S'(12, 16), T'( 12, 16), U'(4, 4)

D S'(12 3 ,4

16 34

), T'( 11 1 ,4

15 14

),

U'(4 3 ,4

4 34

)

6. Polygon K(1, 0), L(8, 3), M(9, 4), N(2, 1) was mapped to polygon O( 1, 1), P(20, 10), Q(23, 13), R(2, 4). What was the similarity transformation? F translate: (x, y) (x 2, y + 1) G first dilate: (x, y) (3x, 3y) then

translate: (x, y) (x – 4, y + 1) H first translate: (x, y) (x – 3, y + 2)

then dilate: (x, y) (0.5x, 0.5y) J translate: (x, y) (x + 0, y + 3)

7. Which similarity postulate or theorem lets you conclude that ABC CDE?

A AA B SAS C SSS D Triangles not similar

Name ________________________________________ Date ___________________ Class __________________




8. What is the length of AC ?

A 10

B 12

C 15

D 20

9. HJJG HJJG

|| .TS PR What is the length of QS ?

A 15

B 20

C 22

D 24

10. Which proportion is correct?

A JX XHGH GJ

B JX GJXH GH

11. If you are using indirect measurement, what is true?

A You must convert dimensions to the same unit of measurement.

B You do not have to convert dimensions to the same unit of measurement.

12. The scale on a map is 1.5 cm : 1280 m. If the distance between the school and the library on the map is 12 centimeters, what is the actual distance between the buildings?

A 15 m

B 150 m

C 9600 m

D 10,240 m

13. Which coordinates for V make SOT UOV?

A (0, 6)

B (4, 0)

C (6, 0)

D (8, 0)

14. ABC has vertices A(0, 0), B(0, 6), and C(4, 0). Which set of coordinates can be used to prove ABC DEF?

A D(0, 0), E(3, 0), F(0, 2)

B D(0, 0), E(0, 3), F(2, 0)

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JKL to MNO is 52


of MN ?

F 6 G 10.8 H 14 J 37.5


A 1.9 cm C 19.2 cm B 3.3 cm D 48 cm



3 3, 4 4

x y has


D S'(12 3 ,4

16 34

), T'( 11 1 ,4

15 14

),

U'(4 3 ,4

4 34

)






Name ________________________________________ Date ___________________ Class __________________





A 10

B 12

C 15

D 20

9. HJJG HJJG


A 15

B 20

C 22

D 24


A JX XHGH GJ

B JX GJXH GH





A 15 m

B 150 m

C 9600 m

D 10,240 m


A (0, 6)

B (4, 0)

C (6, 0)

D (8, 0)


A D(0, 0), E(3, 0), F(0, 2)

B D(0, 0), E(0, 3), F(2, 0)

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JKL to MNO is 52


of MN ?

F 6 G 10.8 H 14 J 37.5


A 1.9 cm C 19.2 cm B 3.3 cm D 48 cm



3 3, 4 4

x y has


D S'(12 3 ,4

16 34

), T'( 11 1 ,4

15 14

),

U'(4 3 ,4

4 34

)






Name ________________________________________ Date ___________________ Class __________________





A 10

B 12

C 15

D 20

9. HJJG HJJG


A 15

B 20

C 22

D 24


A JX XHGH GJ

B JX GJXH GH





A 15 m

B 150 m

C 9600 m

D 10,240 m


A (0, 6)

B (4, 0)

C (6, 0)

D (8, 0)


A D(0, 0), E(3, 0), F(0, 2)

B D(0, 0), E(0, 3), F(2, 0)

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1. Determine whether ABC and DEF are similar. If so, write the similarity ratio and a similarity statement.

_________________________________________

2. Jamestown, North Dakota, claims to have the world s largest bison (American buffalo) statue. The statue is 26 feet high, 46 feet long, and 14 feet wide. The statue is similar to an actual bison that is 6 feet tall. About how long is the actual bison to the nearest foot?

_________________________________________

3. The scale drawing of a triangular swimming pool has the dimensions shown. The longest side of the actual swimming pool is 8 m. What is the length of the actual swimming pool?

_________________________________________

4. Give an example of a transformation that is NOT a similarity transformation.

_________________________________________

5. Describe the dilation

D: (x, y) ĺ § ·¨ ¸© ¹

4 4, .5 5

x y

________________________________________

________________________________________

6. Tell how polygon A(0, 0), B(5, 4), C(3, 2), D(–1, –1) was mapped to polygon E(2, 2.5), F(4.5, 4.5), G(3.5, 3.5), H(1.5, 2).

________________________________________

________________________________________

7. Explain why the triangles are similar and write a similarity statement.

________________________________________

________________________________________

________________________________________

________________________________________

8. Find SP.

________________________________________

Name ________________________________________ Date ___________________ Class __________________




10. Find RQ.

_________________________________________

11. Mentone, Indiana, claims to have the world's largest egg sculpture. A 6-foot-tall person standing next to the egg sculpture casts a shadow that is 2 feet long. If the egg casts a shadow that is 4 feet long, how tall is the sculpture?

_________________________________________

12. A drawing of a garden uses a scale of 1 in : 3 ft. Find the length of the garden if the length on the drawing is 13 inches.

_________________________________________

13. Given that UOV is a dilation image of SOT, find the coordinates of V and the

scale factor.

________________________________________

14. Given: A(0, 0), B(0, 3), C(4, 0), D(0, 6), and E(8, 0) Prove: ABC ADE

________________________________________

________________________________________

________________________________________

________________________________________

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Similarity Chapter Test Form C continued

8. ABC JKL, JL 16, JK x, AC 5x, and AB 125. Find AC.

F 20

G 100

H 125

J Not here

9. What is BY?

A 30 C 52

B 40 D 60

10. An angle bisector of a triangle divides the opposite side of the triangle into segments that are 36 inches and 16 inches long. Another side of the triangle is 60 inches long. What is NOT a possible length for a side of the triangle?

F 2623

in.

G 52 in.

H 135 in.

J Not here

11. Shadows were measured at the same time of day to determine the height of a grain silo. If the silo's shadow measured 15 feet and the height of the silo is 60 feet, which measurements were used to find the height?

A 2-meter pole with a 5-meter shadow

B 5-foot person with a 15-inch shadow

C 10-foot pole with a 40-foot shadow

D 2-meter person with a 3-meter shadow

12. Which scale will produce the smallest drawing?

F 1 cm : 5 m

G 1 mm : 50 m

H 5 cm : 10 m

J 10 cm : 25 m

13. How many different triangles having XY as a side are similar to MNP?

A 2

B 4

C 6

D 10

14. RST has vertices R(1, 1), S(2, 3), and T(5, 1). Which set of coordinates CANNOT be used to prove RST R S T ?

F R (1.5, 1.5), S (3, 4.5), and T (7.5, 1.5)

G R (3, 2), S (5, 6), and T (11, 2)

H R ( 3, 3), S ( 6, 9), and T ( 15, 3)

J R (1, 1), S (2, 1), and T (5, 1)

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44.

45.

46.

47.

48. Determine ifΔJLM ~ΔNPS , if so write a similarity statement and support your answer using transformations.

49. Find the missing measures a) b)

c) d)

50.

51.

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form C

Circle the best answer. 1. Which similarity statement appears to be

true for the figures shown?

A pentagon AEDCB pentagon NMLKJ B hexagon DCBAE hexagon MLKJN C pentagon DCBAE pentagon KJMNL D pentagon DCBAE pentagon MLKJN

2. What is CD if .ABCD . ?TUVW

F 12 H 42 G 28 J 84

3. A scale drawing of a specialized boxing ring has the dimensions shown. The actual ring has the dimension shown. What is the value of x?

A 0.625 ft C 8.1 ft B 1.6 ft D 10 ft

4. Which of the following transformations is NOT a similarity transformation? F M: (x, y) (3x, 4y) G M: (x, y) (5x, 5y) H M: (x, y) (0.01x, 0.01y) J M: (x, y) (0.66x, 0.66y)


1 1, 10 10

x y has

been applied to the polygon V(–6, 4), W(6 , 8), X(–2, –1). What are the coordinates of the image points? A V (60, –40), W (–60, –80),

X (20, 10) B V (–60, 40), W (60, 80),

X (–20, –10) C V (0.6, –0.4), W (–0.6, –0.8),

X (0.2, 0.1) D V (–0.6, 0.4), W (0.6, 0.8),

X (–0.2, –0.1)

6. Polygon S(10, –4), T(–8, 4), U(5, 5), V(8,0) was mapped to polygon W(6, –3.5) X(–3, 0.5), Y(3.5, 1), Z(5, –1.5). What was the similarity transformation? F translate: (x, y) (x – 4, y – 0.5) G translate: (x, y) (x – 3, y – 1.5) H first translate: (x, y) (x 2, y – 3)

then dilate: (x, y) (0.5x, 0.5y) J first dilate: (x, y) (2x, 2y) then

translate: (x, y) (x – 14, y 4.5)

7. Given EK 29

EG and EJ 29

EF, which

similarity postulate or theorem proves EFG EJK?

A AA B SSS C SAS D Not here

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form B continued

8. What is ST?

F 18.75 G 20 H 32.5 J 45

9. What information guarantees that XY AC?

A XB 20, BY 25 B XB 24, BY 30 C XB 25, BY 20 D XB 32, BY 40

10. In JKL, the bisector of J divides intoKL XK with length y 3 and XL

with length 2y. If JK 12 and JL 16, which could be the length of XK ? F 6 G 9 H 12 J 16

11. A student who is 60 inches tall measured shadows to find the height of a tree. The student’s shadow was 24 inches long, and the shadow of the tree was 13 feet long. Which proportion should the student use to find the height of the tree in inches?

A 60 24156 x

C 6024 13

x

B 5 213 x

D 6024 156

x

12. A blueprint uses a scale of 1.5 in : 24 ft. If the actual room has a width of 12 yards and a length of 17 yards, how long is the room on the blueprint?

F 34

in.

G 1 116

in.

H 2 14

in.

J 3 316

in.

13. Which are the coordinates of ABC with vertices A(0, 2), B( 2, 2), and C(2, 4)

after a dilation with a scale factor of 32

?

A A (0, 3), B ( 3, 3), and C (3, 6) B A (0, 1.6), B ( 1.6, 1.6), and

C (1.6, 4.8) C A (0, 3), B (3, 3), and C (3, 6) D A (1.5, 3), B ( 3, 3), and C (3, 6)

14. STU has vertices S(1, 2), T(2, 4), and U(6, 2). Which set of coordinates can be used to prove PQR STU? F P(0.5, 1), Q(3, 1), and R(1, 2) G P(1.5, 3), Q(3, 6), and R(9, 1.5) H P(1.5, 3), Q(3, 6), and R(3, 1) J P(2, 4), Q(4, 8), and R(12, 4)

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Similarity Chapter Test Form C

Circle the best answer. 1. Which similarity statement appears to be

true for the figures shown?

A pentagon AEDCB pentagon NMLKJ B hexagon DCBAE hexagon MLKJN C pentagon DCBAE pentagon KJMNL D pentagon DCBAE pentagon MLKJN

2. What is CD if .ABCD . ?TUVW

F 12 H 42 G 28 J 84

3. A scale drawing of a specialized boxing ring has the dimensions shown. The actual ring has the dimension shown. What is the value of x?

A 0.625 ft C 8.1 ft B 1.6 ft D 10 ft

4. Which of the following transformations is NOT a similarity transformation? F M: (x, y) (3x, 4y) G M: (x, y) (5x, 5y) H M: (x, y) (0.01x, 0.01y) J M: (x, y) (0.66x, 0.66y)


1 1, 10 10

x y has

been applied to the polygon V(–6, 4), W(6 , 8), X(–2, –1). What are the coordinates of the image points? A V (60, –40), W (–60, –80),

X (20, 10) B V (–60, 40), W (60, 80),

X (–20, –10) C V (0.6, –0.4), W (–0.6, –0.8),

X (0.2, 0.1) D V (–0.6, 0.4), W (0.6, 0.8),

X (–0.2, –0.1)

6. Polygon S(10, –4), T(–8, 4), U(5, 5), V(8,0) was mapped to polygon W(6, –3.5) X(–3, 0.5), Y(3.5, 1), Z(5, –1.5). What was the similarity transformation? F translate: (x, y) (x – 4, y – 0.5) G translate: (x, y) (x – 3, y – 1.5) H first translate: (x, y) (x 2, y – 3)

then dilate: (x, y) (0.5x, 0.5y) J first dilate: (x, y) (2x, 2y) then

translate: (x, y) (x – 14, y 4.5)

7. Given EK 29

EG and EJ 29

EF, which

similarity postulate or theorem proves EFG EJK?

A AA B SSS C SAS D Not here

Name ________________________________________ Date ___________________ Class __________________



Similarity Chapter Test Form B continued

8. What is ST?

F 18.75 G 20 H 32.5 J 45

9. What information guarantees that XY AC?

A XB 20, BY 25 B XB 24, BY 30 C XB 25, BY 20 D XB 32, BY 40

10. In JKL, the bisector of J divides intoKL XK with length y 3 and XL

with length 2y. If JK 12 and JL 16, which could be the length of XK ? F 6 G 9 H 12 J 16

11. A student who is 60 inches tall measured shadows to find the height of a tree. The student’s shadow was 24 inches long, and the shadow of the tree was 13 feet long. Which proportion should the student use to find the height of the tree in inches?

A 60 24156 x

C 6024 13

x

B 5 213 x

D 6024 156

x

12. A blueprint uses a scale of 1.5 in : 24 ft. If the actual room has a width of 12 yards and a length of 17 yards, how long is the room on the blueprint?

F 34

in.

G 1 116

in.

H 2 14

in.

J 3 316

in.

13. Which are the coordinates of ABC with vertices A(0, 2), B( 2, 2), and C(2, 4)

after a dilation with a scale factor of 32

?

A A (0, 3), B ( 3, 3), and C (3, 6) B A (0, 1.6), B ( 1.6, 1.6), and

C (1.6, 4.8) C A (0, 3), B (3, 3), and C (3, 6) D A (1.5, 3), B ( 3, 3), and C (3, 6)

14. STU has vertices S(1, 2), T(2, 4), and U(6, 2). Which set of coordinates can be used to prove PQR STU? F P(0.5, 1), Q(3, 1), and R(1, 2) G P(1.5, 3), Q(3, 6), and R(9, 1.5) H P(1.5, 3), Q(3, 6), and R(3, 1) J P(2, 4), Q(4, 8), and R(12, 4)

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Foundations for Geometry Chapter Test Form C

Circle the best answer.

Use the figure for Exercises 1–4.

1. Which is a name for the plane containing

point D?

A plane DB C plane EBD

B plane P D plane FDE

2. Which segment is on plane P but is NOT on line n?

F BE H BC

G GB J AC

3. Which names a pair of opposite rays?

A ABJJJG

and BGJJJG

C ABJJJG

and BAJJJG

B BCJJJG

and ABJJJG

D BDJJJG

and BEJJJG

4. Name the intersection of the two planes.

F line n H line m

G point B J AC

5. R, S, and T are collinear, and S is between R and T. If RS x 1, ST 2x 2, and RT 5x 5, find RT.

A 2 C 5

B 3 D 6

6. Given LM MP, which of the following is always true?

F LM MP

G M is the midpoint of .LP

H M bisects .LP

J L, M, and P are collinear.

7. Find m LMQ.

A 68 C 112

B 90 D 158

8. XZJJJG

bisects WXY, and m WXY 180 . What is m ZXY?

F 45 H 135

G 90 J 180

9. Which angles are adjacent but do NOT form a linear pair?

A 1 and 5 C 2 and 4

B 2 and 3 D 4 and 5

Name ________________________________________ Date ___________________ Class __________________



Foundations for Geometry Chapter Test Form B continued

11. If m B (3x 16) , what is the measure of the supplement of B? A 180 C (164 3x) B (196 3x) D (16 3x)

12. What is the perimeter of a square whose side is 8.2 centimeters? F 16.4 cm H 32.8 cm2 G 32.8 cm J 67.24 cm2

13. What is the area of a triangle with a height of 3 inches and a base of 5.5 inches? A 8.25 in2 C 16.5 in. B 8.5 in2 D 16.5 in2

14. A circle has a diameter of 8 feet. What is its approximate area? F 12.56 ft2 H 50.24 ft2 G 25.12 ft2 J 200.96 ft2

15. Given GH with endpoints G( 11, 4) and H( 1, 9), what are the coordinates of the midpoint of GH ? A ( 12, 5) C ( 10, 13) B ( 6, 2.5) D ( 5, 6.5)

16. M is the midpoint of .RS R has coordinates ( 12, 4), and M has coordinates (1, 2). What are the coordinates of S? F ( 5.5, 1) H (13, 6) G ( 11, 2) J (14, 8)

17. What is the distance from M( 1, 6) to N(11, 1)? A 12 units C 13 units

B 149 units D 169 units

18. What is the distance from V to W?

F 17 cm H 120 cm G 23 cm J 289 cm

19. What transformation is shown?

A rotation C translation B reflection D image

20. Given a point in the coordinate plane, the rule (x, y) (x 2, y 3) translates the point in which direction? F 2 units to the left and 3 units up G 3 units to the left and 2 units down H 3 units right and 2 units up J 2 units to the right and 3 units down

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Foundations for Geometry Chapter Test Form C continued

10. The measure of A is twice the measure of its complement. What is the measure of A? F 20 H 60 G 30 J 90

11. If m B (180 x) , what is the measure of a supplement of B?

A 180 C (180 x)

B x D (90 x)

12. What is the length of a rectangle if the perimeter is 88 inches and the length is 2 inches more than the width? F 21 in. H 25 in. G 23 in. J 42 in.

13. What is the height of a triangle with an area of 16.5 square meters if the base is 5.5 meters? A 1.5 m C 6 m2 B 3 m D 6 m

14. A circle has an area of 81 square feet. What is its radius? F 9 ft H 20.5 ft G 9 ft2 J 40.5 ft

15. Given GH with endpoints G( 7, 3) and H(7, 11), what are the coordinates of the midpoint of GH ?

A (0, 4) C ( 7, 7)

B (0, 8) D ( 14, 14)

16. M is the midpoint of .RS R has coordinates ( 2, 10), and M has coordinates (3, 5). What are the coordinates of S? F (1, 15) H (8, 0)

G (0.5, 7.5) J (5, 5)

17. What is the distance from M(9, 4) to N( 1, 2)?

A 10 C 2 26

B 10 D 12

18. Given a right triangle with the length of one leg equal to 9 centimeters and the length of the hypotenuse equal to 15 centimeters, what is the length of the other leg?

F 6 cm H 306 cm

G 12 cm J 144 cm

19. What transformation is shown?

A rotation C translation B reflection D image

20. A triangle has vertices A( 3, 6), B(1, 5), and C(2, 4). After a transformation, the image of the triangle has vertices A ( 3, 6), B (1, 5), and C (2, 4). Identify the transformation. F reflection across the x-axis G reflection across the y-axis H rotation J translation

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52.

53.

54. Reflect the given figure across the y-‐axis and x-‐ axis

55. Are triangles A(1, 7), B(2, 8), C(3, 7) and D(2.5, 17.5), E(5, 20), F(7.5, 17.5) congruent? Describe the transformation that supports your answer. 56. Find the height ( altitude) of the following triangles a)

b) Given the base is 6cm

c) Find the height when the legs are

57.

58.

59.

60. A map has dimensions 9in. by 15 in.You want to reduce the map so that it will fit on a 4in by 6in index card. What are the dimensions of the largest possible complete map that you can fit on your index card? 61. If you have a vision problem, a magnifiaction system can help you read.You choose a level of magnification.Then you place the image under the viewer.Asimilar magnified image appears on the video screen. A video screen pictured is 16 in wide by 12in tall. What is the largest complete video image possible for a block of text that is 6in wide by 4in. tall? 62.

63.

Name ________________________________________ Date ___________________ Class __________________



Triangle Congruence Chapter Test Form C

Circle the best answer. 1. Describe the transformation M: (x, y) (-y, x).

A A reflection across the y-axis. B A reflection across the x-axis. C A rotation 90 clockwise with center

of rotation (0, 0). D A rotation 90 counterclockwise with

center of rotation (0, 0). 2. Which best describes ABC with vertices

A( 2, 1), B(0, 4), and C(2, 1)? F acute H obtuse G equiangular J right

3. Which is a correct classification of DEF with vertices D( 3, 2), E( 2, 3), and F(1, 0)? A equilateral C scalene B isosceles D Not here

4. What is the value of x?

F 41 H 99 G 58 J 122

5. QRS STQ, QS x2 10 and SQ 2x 2. What is the value of x? A 4 C 2 B 2 D 4

6. ABC DEF. What information is NOT needed to find the perimeter of ABC if you are given all four lengths below?

F DE H CF G BG J EF

Use the partially completed two-column proof for Exercise 7. Given:

Prove: GHF MOL

Proof:

Statements Reasons

1. ,

,

GF ML

FH LO

GH MO

1. Given

2. F L 2. ?

3. H O 3. Given

4. G M 4. ?

5. GHF MOL 5. ?

7. Which reason does NOT belong in the proof? A Def. of s B Third s Thm. C Rt. Thm. D CPCTC

Use the figure for Exercises 8–11.

8. AB y 3, DC 3y 1, EB 3y 1, ED y 1, AE y, CE 2y. What value of y proves

AEB CED by the SSS Postulate? F 2 H 1 G 1 J 2

Name ________________________________________ Date ___________________ Class __________________



Triangle Congruence Chapter Test Form B continued

11. If B and C are right angles, what additional congruence statement would allow you to prove DCB ABC by the ASA postulate? A DBC ACB B BDC CAB

C AB DC

D AC DB 12. If A and C are right angles and

AD BC , what postulate or theorem justifies the congruence statement BCD DAB?

F SAS H AAS G ASA J HL

13. A right triangle with leg lengths of 4 and 3 units has to be positioned in the coordinate plane to write a coordinate proof. Which set of coordinates would make the proof easier to complete? A (4, 0), (0, 0), (4, 3) B (3, 0), (0, 0), ( 4, 0) C (0, 4), (0, 0), ( 3, 0) D (0, 4), (0, 0), (3, 0)

14. Which of the following would you find most useful in giving a coordinate proof that two triangles are congruent by SSS? F Distance Formula G Midpoint Formula H CPCTC J Slope Formula

15. What is the value of x?

A 12 C 18 B 19.5 D 60

Use the partially completed two-column proof for Exercises 16–18.

Given: GJ bisects FGH, FG HG

Prove: FJ HJ Proof:

16. Which reason belongs in Step 4? F Isosc. Thm. G Conv. of Isosc. Thm. H ASA J Def. of bisector

17. Which reason belongs in Step 5? A Isosc. Thm. C CPCTC B ASA D HL

18. Which reason belongs in Step 6? F Isosc. Thm. G ASA H CPCTC J Def. of bisector

Statements Reasons

1. GJ bisects FGH. 1. Given

2. FGJ HGJ 2. Def. of bisector

3. FG HG 3. Given

4. F H 4. ?

5. FGJ HGJ 5. ?

6. FJ HJ 6. ?

Chapter

x

71

Chapter

4

71

CS10_G_MEAR710334_C04MCCT.indd 71 4/5/11 6:14:16 PM

Name ________________________________________ Date ___________________ Class __________________



Transformational Geometry Chapter Test Form A

Circle the best answer. 1. Is the transformation a reflection?

A yes

B no

2. When the point ( 3, 2) is reflected across

the y-axis, what is the resulting image?

A ( 3, 2)

B (3, 2)

C (2, 3)

D (3, 2)

3. Is the transformation a translation?

A yes

B no

4. What is the image of (3, 6) when it is

translated along the horizontal vector

¢ 2, 0²?

A (3, 4)

B (1, 4)

C (1, 6)

D (5, 6)

5. Is the transformation a rotation?

A yes

B no

6. What is the image of (5, 4) when it is

rotated 180 about the origin?

A ( 5, 4)

B ( 4, 5)

C ( 5, 4)

D (4, 5)

7. If LM is reflected across the x-axis and

then translated along the vector ¢4, 1², in which quadrant is the final image?

A Quadrant I

B Quadrant II

C Quadrant III

D Quadrant IV

8. The composition of two reflections

across parallel lines is equivalent to

which type of transformation?

A translation

B rotation

Chapter

x

167

Chapter

9

167


240 Chapter 4 Congruent Triangles

USING ALGEBRA Find the value of x.

17. 18. 19.

USING ALGEBRA Find the values of x and y.

20. 21. 22.

23. 24. 25.

PROOF In Exercises 26–28, use the diagrams that accompany thetheorems on pages 236 and 237.

26. The Converse of the Base Angles Theorem on page 236 states, “If two anglesof a triangle are congruent, then the sides opposite them are congruent.”Write a proof of this theorem.

27. The Corollary to Theorem 4.6 on page 237 states, “If a triangle is equilateral,then it is equiangular.” Write a proof of this corollary.

28. The Corollary to Theorem 4.7 on page 237 states, “If a triangle is equiangular,then it is equilateral.” Write a proof of this corollary.

ARCHITECTURE The diagram represents part of the exterior of the building in thephotograph. In the diagram, ¤ABD and ¤CBDare congruent equilateral triangles.

29. Explain why ¤ABC is isosceles.

30. Explain why ™BAE £ ™BCE.

31. PROOF Prove that ¤ABEand ¤CBE are congruent righttriangles.

32. Find the measure of ™BAE.

60!

x !

y !40!

x !

y !

x !

y !

140!x !

y !

75!

x !

x !

y !y !x !

xyxy

56 ft

8x ft

12 in.

2x in.(x + 13) ft 24 ft

xyxy

A

C

B DE

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GeometryID: 1

Seat No.______ Period____Date________________©D G2v0a1o32 WK6u8tpar tS3obfotIwRaGr8ek TLILUCa.7 0 dAhlNlL trjiigNhltFsb krre0saeirRvVeodo.kIsosceles Triangles

Find the value of

x.

1) 75°

x

2) 30°

x

3)

98°

x

4) 43°

x

5)

54°

x

6)

50°

x

7)

51°

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8)

33°

x

9)

38°

x

10)

73°

x

11)

80°

x

12)

44°

x

13)

45°

x

14) 41°

x

Print to PDF without this message by purchasing novaPDF (http://www.novapdf.com/)

©k q2s0R1g3C IKDupt0a2 ESEozfxtowOaKrrel SLkL6Co.v k GAMlalF 4rQi2gfhDtSs2 DrKe1sZeUrEvNehdo.7 a nM8aCdNeC Awvi8tBhr uIrnff9iInXiEtoeT 3GLejofmXe1terBy9.d Worksheet by Kuta Software LLC

GeometryID: 1

Seat No.______ Period____Date________________©D G2v0a1o32 WK6u8tpar tS3obfotIwRaGr8ek TLILUCa.7 0 dAhlNlL trjiigNhltFsb krre0saeirRvVeodo.kIsosceles Triangles

Find the value of

x.

1) 75°

x

2) 30°

x

3)

98°

x

4) 43°

x

5)

54°

x

6)

50°

x

7)

51°

x

8)

33°

x

9)

38°

x

10)

73°

x

11)

80°

x

12)

44°

x

13)

45°

x

14) 41°

x

Print to PDF without this message by purchasing novaPDF (http://www.novapdf.com/)

Name ________________________________________ Date ___________________ Class __________________



Triangle Congruence Chapter Test Form A

Circle the best answer. 1. The transformation: (x, y) (x 5, y

7) is a __________. A Translation B Reflection C Rotation D Dilation

2. What type of triangle is ABC?

A acute B equiangular C obtuse D right

3. How many sides must be congruent in an isosceles triangle? A at least 2 B all 3

4. Which pair of angle measures CANNOT be the acute angles of a right triangle? A 29 and 61 B 30 and 60 C 38 and 53 D 45 and 45

5. What is m ACD?

A 100 B 130

6. If KLM RST, find the value of x.

A 18 B 45

7. Given: A D, B E, C F, ,AB DE ,BC EF

and .CA FD Which is a correct congruence statement? A BCA DEF B ABC DEF

Use the figure for Exercises 8 and 9.

8. Which value for x proves that ABC DEF by SSS?

A 7 B 37

9. What additional information would allow you to prove the triangles congruent by SAS? A E D B D C C D A D F C

Chapter

x

67

Chapter

4

67


64.

65.

66.

67.

68.

69.

70.

71.

72.

778 Chapter 11 Circles

The Winchester Round Table, probably built in the late thirteenth century, is 18 ft across and weighs 1.25 tons. King Arthur’s Round Table of English legend would have been much larger—it could seat 1600 men.

History

30. Given: ∠ABC is inscribed in ⊙X with X in the interior of ∠ABC.Prove: m∠ABC = 1 _

2 m # AC

(Hint: Draw $$% BX and use Case 1 of the Inscribed Angle Theorem.)

31. Given: ∠ABC is inscribed in ⊙X with X in the exterior of ∠ABC.Prove: m∠ABC = 1 _

2 m # AC

32. Prove Corollary 11-4-2. Given: ∠ACB and ∠ADB intercept # AB .Prove: ∠ACB & ∠ADB

33. Multi-Step In the diagram, m # JKL = 198°, and m # KLM = 216°. Find the measures of the angles of quadrilateral JKLM.

34. Critical Thinking A rectangle PQRS is inscribed in a circle. What can you conclude about −− PR ? Explain.

35. History The diagram shows the Winchester Round Table with inscribed △ABC. The table may have been made at the request of King Edward III, who created the Order of Garter as a return to the Round Table and an order of chivalry.

a. Explain why −−

BC must be a diameter of the circle.

b. Find m # AC .

36. To inscribe an equilateral triangle in a circle, draw a diameter

−− BC . Open the compass to the radius of the circle.

Place the point of the compass at C and make arcs on the circle at D and E, as shown. Draw −− BD , −− BE , and −− DE . Explain why △BDE is an equilateral triangle.

37. Write About It A student claimed that if a parallelogram contains a 30° angle, it cannot be inscribed in a circle. Do you agree or disagree? Explain.

38. Construction Circumscribe a circle about a triangle. (Hint: Follow the steps for the construction of a circle through three given noncollinear points.)

39. What is m∠BAC? 38° 66° 43° 81°

40. Equilateral △XCZ is inscribed in a circle. If −−

CY bisects ∠C, what is m # XY ? 15° 30° 60° 120°

41. Quadrilateral ABCD is inscribed in a circle. The ratio of m∠A to m∠C is 4 : 5. What is m∠A?

20° 40° 80° 100°

42. Which of these angles has the greatest measure? ∠STR ∠QPR ∠QSR ∠PQS

ge07se_c11_0772_0779.indd 778ge07se_c11_0772_0779.indd 778 6/1/06 4:07:52 PM6/1/06 4:07:52 PM

Name Date Class



Circles Chapter Test Form C

Circle the best answer. 1. Which is never a chord?

I diameter II radius III secant IV tangent A I and II C II and IV B III and IV D I, II, and III

2. A mountain climber is standing at the top of Mount Everest. The distance from the summit to the horizon is about 210 miles. About how high is Mount Everest?

F 5.5 mi H 210 mi G 11 mi J 8000 mi

3. Which is pmBA ?

A 80 C 128 B 120 D 140

4. Which is the area of UABD?

F 10 m2 H 75 m2 G 62.5 m2 J 125 m2

5. A slice of cake is a sector of a cylinder. To the nearest hundredth, what is the volume of the piece of cake? Use 3.14 for .

A 26.17 cm3 C 196.25 cm3 B 39.25 cm3 D Not here

6. If the length of pTU is 6 , what is the radius of the circle?

F 2.4 H 15 G 5.48 J 47.1

7. Which is m VXU?

A 105 C 122.5 B 120 D 126

8. What is m TQR?

F 65 H 110 G 70 J 115

Name Date Class



Circles Chapter Test Form C continued

9. If m FAE 65 , m AFD 35 , pm 60 ,AB and FA and GC are

tangent to the circle, what is m AGC?

A 65 C 80 B 70 D Not here

10. What is m LYK?

F 12 H 98 G 66 J Not here

11. What is pmPQ ?

A 50 C 150 B 115 D 200

12. What is the length of RP ?


13. What is the length of SQ ?

A 4 C 9 B 9 D Not here

14. What is the length of the diameter?


15. For which value(s) of the constant k is the circle x2 (y k)2 16 tangent to the line y 3? A 1 only C 1 B 1 and 7 D 1 and 7

16. Which is the equation of a circle that has a diameter with endpoints (1, 3) and ( 3, 1)? F (x 1)2 (y 2)2 10 G (x 1)2 (y 2)2 20 H (x 1)2 (y 2)2 5 J (x 1)2 (y 2)2 5

17. A new firehouse is being built equidistant from three other fire stations. Positioned on a grid, the current fire stations would be located at (3, 7), ( 1, 1), and ( 4, 8). What are the coordinates of the location where the new firehouse should be built? A ( 1, 4) C (1, 4) B ( 1, 4) D (1, 4)

Chapter

x

224

Chapter

12

224


Name Date Class



Circles Chapter Test Form B

Circle the best answer. 1. Which is a chord?

A AE C BD

B HJJGBE D OC

2. A plane is cruising at an altitude of 30,000 feet. What is the distance, to the nearest mile, from the plane to the horizon?

F 213 mi H 8,500,000 mi G 4000 mi J Not here

3. Which of these arcs has a measure of 134 ?

A pFJ pEG

B pDF qDH 4. What is BD?

F 7.5 H 9.4 G 8.5 J 15

5. Which sector does NOT have an area of 3 ?

A central angle 135 ; radius 2 2 B central angle 80 ; radius 3 C central angle 67.5 ; radius 4 D central angle 270 ; diameter 4

6. Which arc has a length of 5 units? F arc measure 45 ; radius 10 G central angle 90 ; radius 10 H arc measure 90 ; radius 5 J central angle 45 ; diameter 20

7. What is m VXU?

A 30 C 65 B 45 D 105

8. Quadrilateral PQRS is inscribed in a circle. The ratio of m P to m R is 2 : 4. What is m R? F 30 H 120 G 60 J Not here

9. What is m JKM?

A 28 C 90 B 58.5 D 117

Name Date Class



Circles Chapter Test Form B continued

10. What is m JBM?

F 50 H 110

G 80 J 150

11. How many arc degrees are in the

minor arc?

A 32.5 C 115

B 65 D Not here

12. What is the length of SQ ?

F 5 H 13

G 9 J 17

13. If RQ 8, what is the length of RP ?

A 3

B 5

C 13.5

D Not here

14. Hikers came across a part of a redwood

stump. If the length of the chord is 8 feet,

what was the diameter of the tree?

F 4 ft H 8 ft

G 5 ft J 10 ft

15. Which is the equation of a circle that

passes through (2, 2) and is centered

at (5, 6)?

A (x 6)2 (y 5)2 25

B (x 5)2 (y 6)2 5

C (x 5)2 (y 6)2 25

D (x 5)2 (y 6)2 25

16. Which is the graph of

(x 1)2 (y 2)2 4?

F H

G J

17. A hospital trauma center is going to be

built equidistant from three cities.

Positioned on a grid, the cities would be

located at (1, 5), (2, 2), and ( 6, 2).

What are the coordinates of the location

where the trauma center should be built?

A ( 2, 1) C (2, 1)

B ( 2, 1) D (2, 1)

Chapter

x

222

Chapter

12

222


Name ________________________________________ Date ___________________ Class __________________



Right Triangles and Trigonometry Chapter Test Form C

Circle the best answer.

1. UABC is a right triangle with hypotenuse .AB The altitude to the hypotenuse is ,CD and CD 24. If the length of the

shortest leg of UABC equals 30, what is the length of the hypotenuse? A 32 C 50 B 40 D Not here

2. If DA 4(BD), what is the perimeter of UABC in simplest form?

F 55 H 40 5

G 25 15 5 J Not here

3. Which is NOT a sine, cosine, or tangent value, rounded to the nearest hundredth, for A?

A 0.55 C 0.86 B 0.63 D 1.58

4. Which is NOT true?

F sin 30 cos 30°tan 30°

G cos60 (tan60 ) cos30 H tan45 1 J sin60 (tan30 ) cos45

5. Which expression CANNOT be used to find BC?

A 7.8(sin23 ) B 7.8(cos67 ) C 7.8(tan23 )

D 7.2tan 67

6. What is XZ? Round to the nearest unit.


7. The coordinates of the vertices of UJKL are J( 2, 3), K(2, 3), and L(2, 2). Find the measure of J to the nearest degree. A 36 C 51 B 39 D 54

8. Suppose A is one of the acute angles formed by the line x 2y 6 and the x-axis. What is the approximate measure of A? F 27 G 30 H 60 J 63

Name ________________________________________ Date ___________________ Class __________________



Right Triangles and Trigonometry Chapter Test Form B continued

9. A utility worker is installing a 25-foot telephone pole. The work order indicates that two guy wires (a wire running from the ground to the top of the pole) should be placed opposite each other and at a 65 angle of elevation to the pole. To the nearest tenth of a foot, how far apart are the guy wires? If necessary, compute any trigonometric ratios at least to the nearest hundredth. A 11.7 ft C 27.6 ft B 23.3 ft D Not here

10. A forest ranger in a 140-foot observation tower sees a fire moving in a direct path toward a lake. The angle of depression to the fire is 3 , and the angle of depression to the lake is 8 . To the nearest foot, how close is the fire to the base of the observation tower? (The figure is not drawn to scale.)

F 997 ft H 2671 ft G 1675 ft J Not here

11. What information makes it possible to find the remaining measures in UABC using the Law of Sines?

A AC 13, m A 62 , AB 6 B AC 13, m B 88 , AB 6 C AC 13, AB 6, BC 11 D m A 63 , m B 88 ,

m C 29

12. Which expression can be used to find m R?

F cos 1§ ·¨ ¸© ¹

144

G cos 414

§ ·¨ ¸© ¹

H cos 14

14§ ·¨ ¸© ¹

J cos 14

14§ ·¨ ¸© ¹

13. Which vector has a magnitude, to the nearest tenth, of 3.6? A ¢4, 2² B ¢1, 3² C ¢3, 2² D ¢4, 2²

14. Which vector is NOT parallel to ¢10, 6²? F ¢ 10, 6² G ¢3, 5² H ¢5, 3² J ¢12, 7.2²

15. A kayaker paddles across a river at a constant speed of 4 miles per hour and a bearing of N 60 E. Which current vector results in the kayaker’s actual speed being 5.9 miles per hour and the kayaker’s actual direction being N 70 E? If necessary, round speed to the nearest tenth and direction to the nearest degree. A ¢1, 0² B ¢2, 0² C ¢2.5, 0² D ¢3, 0²

Chapter

x

150

Chapter

8

150


73.

74.

75. PROOFS 1.

2.

3.

4.

5.

6.

7.

8.

Documents

Chapter Test x 7 Form A continued Chapter TestSimilarity Form A …caronnaclassroom.weebly.com/uploads/1/3/3/8/13388109/... · 2019. 8. 24. · 46 feet long, and 14 feet wide. The