CHAPTER Standardized Test A 5 For use after Chapter 5

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GeometryChapter 5 Assessment Book96

Multiple Choice

1. Every triangle has ? midsegments.

A at least 1 B exactly 1

C at least 2 D exactly 3

2. If } BD , } DF , and } FB are midsegments of TACE, what is AF?

A 10 B 15 C 20 D 30

3. If @###$ MN is the perpendicular bisector of } RJ , what is RM?

A 8 B 9 C 17 D 19

4. In the fi gure, the perpendicular bisectors of TBFG meet at point A. What is AF?

A 12 B 16 C 20 D 22

5. In the fi gure, AP 5 5x and BP 5 3x 1 4. For what value of x does P lie on the bisector of aB?

A 2 B 4 C 6 D 10

6. Point N is the intersection of the angle bisectors of TABC. What is NE?

A 4 B 5 C 6 D 12

7. A(n) ? of a triangle is a segment from a vertex to the midpoint of the opposite side.

A median B midsegment

C altitude D angle bisector

8. What is AP in the fi gure below?

A 16 B 18 C 24 D 36

CHAPTER

5 Standardized Test AFor use after Chapter 5

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GeometryChapter 5 Assessment Book 97

Standardized Test A continuedFor use after Chapter 5

9. What is the shortest side of nXYZ?

A } XY

B } XZ

C } YZ

D cannot be determined

10. Which is a possible value of x?

A 7

B 9

C 11

D 18

11. Using the Hinge Theorem, which can be concluded from the diagram?

A AC 5 DE

B AC . DF

C DF > BC

D DF > AC

12. Based on the diagram, which is a true statement?

A m∠ 1 5 m∠ 2

B m∠ 1 < m∠ 2

C m∠ 1 > m∠ 2

D }

GK bisects ∠ JGH.

Gridded Response

13. Point Q is the intersection of the medians of nDEF. What is ME 2 DP?

Short Response

14. In nCRM, CR 5 6 and RM 5 11. Write inequalities to show all the possible values for CM.

Extended Response

15. From a lookout tower, Fire 1 is located 9 miles due north and Fire 2 is located 12 miles due east.

a. Find the shortest distance fi refi ghters can travel from Fire 1 to Fire 2. Explain.

b. A campground is located halfway between the lookout tower and Fire 1, and another campground is located halfway between the lookout tower and Fire 2. Explain how the answer from part (a) can be used to fi nd the distance between the campgrounds. Then fi nd the distance.

c. A fi re truck is located in the middle of the shortest path between the two fi res. It heads towards the campground located between the lookout tower and Fire 2. How far must it travel to reach the campground? Explain.

CHAPTER

5


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Multiple Choice

1. The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is ? .

A twice as long B half as long

C one third as long D the same length

2. If }

RS , } RT , }

ST , } WY , } WZ , and } YZ are all midsegments, fi nd x.

F GR

YW

S Z T

H

3x

6

A 1 }

2 B 2 C 3 D 1

3. If }

QS is the perpendicular bisector of } PR , fi nd RS.

x

y

P (0, 2)

S (3, 0)

R

A 3 }

2 B Ï

}

13 C Ï}

5 D 5 }

2

4. By the Concurrency of

D K

E

F

J

L

Perpendicular Bisectors Theorem, if

} QJ , }

QK , and }

QL are perpendicular bisectors, then ? .

A ∠ JQK > ∠ KQL > ∠ LQJ

B DE 5 EF 5 FD

C QD 5 QE 5 QF

D ∠ EQK > ∠ FQL > ∠ DQJ

5. Point A is the incenter of nFGH. Find AS.

A 3

3

5F

T

R

A

H

G

S

B 2

C 4

D 5

6. Given the inscribed circle with center K, which statement can you not conclude?

X ZO

K

N

Y

M

A XK 5 YK B ∠ NZK > ∠ OZK

C } NK ⊥ } YZ D MK 5 OK

7. The point of concurrency of the three medians of a triangle is called the ? of the triangle.

A tri-sector point B centrino

C median point D centroid

8. If point P is the centroid of nABC, fi nd CP.

A (6, 1) B (10, 1)

C (5, −3)

P

A 5 B 10

} 3 C

5 }

3 D

7 }

3

9. Which is the longest side of nDEF?

A } DE D E

F

70°

80°

B } DF

C } EF

D cannot be determined

CHAPTER

5 Standardized Test BFor use after Chapter 5


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Standardized Test B continuedFor use after Chapter 5

10. Which is a possible value of x?

A 2

8

5 x

B 4

C 14

D 17

11. Using the Hinge Theorem and the diagram, you can conclude:

60°

120°L

M S

K

P

A m∠ KLM < m∠ QSP

B QS 5 LM

C PS > LM

D none of these

12. Based on the diagram, which is a true statement?

B

A

C

D

E

6

5

A m∠ A > m∠ D

B m∠ A < m∠ D

C m∠ A 5 m∠ D

D E is the midpoint of }

BC .

Gridded Response

13. R is the centroid of nMNP and JP 5 21. Find the perimeter of nMJR.

9

18M J N

R

L K

P

Short Response

14. In nPQR, PQ 5 20 and PR 5 9. Write an inequality to show all possible values for QR.

Extended Response

15. A campground has a convenience store located 100 yards due south of the shower facilities. There is a game room 100 yards due east of the convenience store.

a. Camper A leaves the game room for the shower. What is the shortest travel distance possible?

b. Camper B is doing laundry half way between the game room and the convenience store. Find the shortest distance Camper B can travel to get to the pool located half way between the store and the shower.

c. Camper C is lost, standing at the convenience store facing west. If his tent is equidistant from the store, the shower, and the game room, provide two-step instructions to get Camper C back to the tent.

CHAPTER

5

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Multiple Choice

1. Triangle DEF is formed by connecting the midpoints of TABC. The perimeter of TDEF is 24. What is the perimeter of TABC?

A 12 B 36 C 48 D 72

2. In the diagram, HP 5 x 1 3, MN 5 2x 2 6, and MP 5 x 1 5. Find GK.

A 12 B 14 C 24 D 28

3. If } UW is the perpendicular bisector of } TV , fi nd UV.

A Ï}

5 B 3 Ï}

2 C 3 Ï}

5 D Ï}

37

4. Which must be true given that C is the circumcenter of TGHK?

A CH 5 CK 5 CG B CR 5 CS 5 CT

C CH 5 1 }

2 CK D CR 5

2 }

3 RK

5. Point M is the incenter of TXYZ. Find MC.

A 12 B 15 C 31 D 35

6. Which method could have been used to inscribe the circle inside the triangle?

A Find the incenter P, then use PA as the radius.

B Find the incenter P, then use PQ as the radius.

C Find the circumcenter P, then use PA as the radius.

D Find the circumcenter P, then use PQ as the radius.

7. Which statement is not always true?

A The medians of a triangle intersect inside the triangle.

B The altitudes of a triangle intersect inside the triangle.

C A median of a triangle intersects a vertex of the triangle.

D An altitude of a triangle intersects a vertex of the triangle.

CHAPTER

5 Standardized Test CFor use after Chapter 5


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Standardized Test C continuedFor use after Chapter 5

8. Given that P is the centroid of TABC, fi nd PD.

A 10

} 3 B

20 }

3 C 5 D 10

9. In TPTR, m∠ P 5 55° and m∠ R 5 45°. Which list gives the sides in order from shortest to longest?

A } PR , } RT , } PT B } RT , } PT , } PR

C } PT , } PR , } RT D } PT , } RT , } PR

10. Which can be the measures of the sides of a triangle?

A 3 cm, 4 cm, 7 cm

B 4 cm, 6 cm, 8 cm

C 5 cm, 5 cm, 12 cm

D 6 cm, 7 cm, 15 cm

11. Given that L is the midpoint of } JN , which can be concluded from the diagram?

A KL , ML

B KL . ML

C KL 5 ML

D KL , LN

12. By the Hinge Theorem, which inequality gives the correct restriction on x?

A x , 3

B x . 3

C x , 9

D x . 9

Gridded Response

13. Point A is the centroid of TDEF. Find the perimeter of TADN.

Short Response

14. In nSTR, ST 5 23.6 and TR 5 31.5. Write an inequality to show all the possible values for SR.

Extended Response

15. A cargo ship travels due north from a port at a rate of 15 miles per hour while a cruise ship leaves the port at the same time, traveling due east at 20 miles per hour.

a. Both ships stop after three hours. What is the shortest distance between the ships? Explain.

b. There is an island 45 miles due north of the cargo ship and another island 60 miles due east of the cruise ship. Ex-plain how the answer from part (a) can be used to fi nd the shortest distance between the islands.

c. A sailboat is equidistant from the two islands and the port. What is the short-est distance between the sailboat and the cargo ship? the sailboat and the port? the sailboat and the cruise ship?

CHAPTER

5


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A9Geometry

Assessment Book

illustrates the student’s explanation of when to use the method.

2. a. nABD and nCBD are scalene right triangles; nABC is an acute isosceles triangle; nEFG is an obtuse scalene triangle b. It is given that nABD and nCBD are right triangles and }

AB > }

CB . By the Refl exive Property, } BD > } BD . So, by the HL Congruence Theorem, nABD > nCBD. c. ∠BAD > ∠BCD; ∠ABD > ∠CBD; ∠ADB > ∠CDB;

} AB >

} CB ;

} BD > } BD ;

} AD >

} CD d. 1148

e.

x

y

1

1

C(21, 1)

A(23, 0)

E(0, 4)

F(1, 1)

D(3, 0)

B(0, 4)

f. refl ection in y-axis g. Sample answer: Use the Distance Formula to fi nd the side lengths of all three triangles. Then use the SSS Congruence Postulate.

Chapter 5Quiz 1

1. 19 2. 12 3. 8 4. 10; Perpendicular Bisector Theorem 5. 14; Concurrency of Perpendicular Bisectors Theorem

Quiz 2

1. 7 2. 7 3. 6 4. 12 5. 4

Quiz 3

1. yes 2. No, 4 1 7 < 13. 3. 1 < x < 11

4. 7 < x < 35 5. }

BC , }

AC , }

AB

6. ∠ D, ∠ E, ∠ F 7. < 8. 5

Chapter Test A

1. 68 2. 11 3. 12 4. 7.5 5. (2h, 0)

6. 1 h } 2 , k 2 7. 8 8. 2 9. 15 10. 20 11. 18

12. 9 13. }

RS , }

RQ , }

QS 14. ∠B, ∠A, ∠C

15. yes 16. no 17. no 18. < 19. >

20. C, B, A, D

Chapter Test B

1. 50 2. 30 3. 7 4. 3 } 4

5.

x

y

1

1

6.

x

y

1

1

(0, 0), (0, 3), (3, 0) (0, 0), (0, 2), (3, 2), (3, 0)

7. 5 8. 9 9. 10 10. 25 11. 6 12. 3

13. }

BC , }

AB , }

AC 14. }

QS , }

QR , }

RS

15. 4 < x < 16 16. < 17. > 18. x ≤ 15

Chapter Test C

1. 32 2. 22 3. 18 4. x 5 10 5. x 5 48

6. x 5 5 7. x 5 7 8. (2, 21) 9. (21, 21)

10. x 5 7 11. x 5 5 12. x 5 9 }

2

13. Check students’ drawings 14. }

BC , }

AC , }

AB

15. ∠G, ∠F, ∠H

16. yes; ∠C, ∠A, ∠B 17. no 18. <

19. 5 20. x < 21 21. x < 9 }

2

Standardized Test A

1. D 2. B 3. D 4. C 5. A 6. B 7. A 8. C

9. A 10. A 11. D 12. B 13. 6

14. CM . 5 and CM , 17

15. a. By the Pythagorean Theorem, the distance

is Ï}

92 1 122 5 15 miles. b. The tower and the

fi res form a triangle and the shortest distance between the campgrounds is a midsegment of the triangle. It is parallel to the side measuring 15 miles, so its distance is 7.5 miles. c. 4.5 miles; The path is the midsegment that is parallel to the side between the tower and Fire 1, which measures 9 miles.

Standardized Test B

1. B 2. D 3. B 4. C 5. A 6. A 7. D

8. B 9. A 10. B 11. C 12. A 13. 43

14. 11 < QR < 29 15. a. 141.4 yd b. By the Pythagorean Theorem, a2 1 b2 5 c2, so 502 1 502 5 c2 and c < 70.7. By the Midsegment Theorem, because the pool and laundry room are midpoints, the distance from the laundry room to the pool is half the distance from the game room to the shower. c. Turn clockwise 1358 and walk forward 70.7 yards.

Chapter 4, continuedA

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A10GeometryAssessment Book

Standardized Test C

1. C 2. D 3. C 4. A 5. C 6. B 7. B 8. A

9. D 10. B 11. A 12. B 13. 28.45

14. 7.9 , x , 55.1

15. a. By the Pythagorean Theorem, the distance

is Ï}

452 1 602 5 75 miles. b. The islands and

the port form a triangle where the ships’ current locations are midpoints of two sides, making the shortest path between the ships a midsegment of the triangle. The shortest distance between the islands is parallel to this side and twice as long, so the distance is 150 miles. c. 60 miles; 75 miles; 45 miles

SAT/ACT Chapter Test

1. A 2. B 3. E 4. C 5. D 6. A 7. D 8. A

9. B 10. C 11. E 12. 18 13. 41

Performance Assessment

1. Complete answers should include: an explanation that a coordinate proof involves placing geometric fi gures in a coordinate plane; an explanation that when variables are used to represent the coordinates of a fi gure in a coordinate proof, the results are true for all fi gures of the given type; an example of a coordinate proof; an explanation that an indirect proof involves the assumption that the desired conclusion is false and that this original assumption must be shown to be impossible; an example of an indirect proof.

2. a. (65, 50) and (100, 50) b. 35 units c. No. Because the triangle is obtuse, the circumcenter will lie outside of the rose garden. d. about (70, 30) e. about (20, 110) f. about (177, 110) g. The length of the third side must be less than 7 feet and greater than 1 foot.

Chapter 6Quiz 1

1. x 5 6 2. s 5 15 3. a 5 10 4. 9 } 7

5. 8 } 12

or 2 }

3 6.

y 1 7 } 7 7. 11.2

Quiz 2

1. 2 : 1 2. 18 3. 28 4. 122 5. 164, 82

6. 1, 2, 3, 5 7. 2 }

1 5 2,

3 }

2 5 1.5,

5 }

3 ø 1.667

8. similar; n ABC , nDEF 9. not similar

10. similar; nPQR , nTSR

Quiz 3

1. 27 2. 20 3. 42

4.

x

y

1

1

5. x

y

222

Chapter Test A

1. 17

} 2 2.

4 }

1 3.

8 }

1 4.

40 }

1 5. x 5 24 6. x 5 14

7. x 5 1 8. x 5 5 9. 12 10. 20 11. 6 Ï}

10

12. 15 13. 18 14. similar; JKLM , PQRS, 2 } 5

15. similar; nTUV , nXYZ, 4 }

3

16. similar; nABC , nGFH 17. not similar

18. not similar 19. similar; nDHG , nFHE

20. x 5 12 21. x 5 24 22. x 5 28 23. x 5 26

24. 3 25. 1 } 10

26. length 5 140 m, width 5 80 m

Chapter Test B

1. 5 : 1 2. 20

} 1 3.

528 }

1 4.

9 }

1 5. 30 : 1 6.

3 }

1

7. 4.5 8. 5 9. 5 10. 24

11. nABD , nECD; AA Similarity Postulate

12. no 13. 22.5 14. 95 15. 1.5 16. 12

17. 2 18. 1 } 12

19. 8 in., 4 in. 20. 26 in., 6.5 in. 21. 5 ft

Chapter Test C

1. 4 }

9 2.

1 } 5 3.

24 }

1 4. x 5 14 5. x 5 24

6. x 5 7 7. 39

} 5 8. 320

} 31

9. 4 m 10. 8 } 5

11. 11 1 } 5 12. LM 5 8.1, PQ 5 13.0

13. 55, 89, 144, 233

14. 89

} 55 ø 1.6182, 144

} 89

ø 1.6179, 233

} 144

ø 1.6181

15. similar; nABE , nCBD 16. not similar

17. similar; nJKL , nJMN

18. similar; nEHD , nGHF

19. x 5 16 20. x 5 7

Chapter 5, continuedA

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CHAPTER Standardized Test A 5 For use after Chapter 5