Standardized Test A For use after Chapter 5

Transcription

1 Standardized Test A For use after Chapter Multiple Choice. Ever triangle has? midsegments. A at least B eactl C at least D eactl. If BD, DF, and FB are midsegments of TACE, what is AF? A 0 B C 0 D 0. MN is the perpendicular bisector of RJ, what is RM?. In the figure, AP and BP 4. For what value of does P lie on the bisector of ab? A B 4 C 6 D 0 6. Point N is the intersection of the angle bisectors of TABC. What is NE? A 4 B C 6 D 7. A(n)? of a triangle is a segment from a verte to the midpoint of the opposite side. A 8 B 9 C 7 D 9 4. In the figure, the perpendicular bisectors of TBFG meet at point A. What is AF? A median B midsegment C altitude D angle bisector 8. What is AP in the figure below? A 6 B 8 C 4 D 6 A B 6 C 0 D 96 Chapter Assessment Book

2 Standardized Test A continued For use after Chapter 9. What is the shortest side of nxyz? Gridded Response A XY B XZ C YZ D cannot be determined 0. Which is a possible value of? A 7 B 9 C D 8. Point Q is the intersection of the medians of ndef. What is ME DP? Short Response 4. In ncrm, CR 6 and RM. Write inequalities to show all the possible values for CM.. Using the Hinge Theorem, which can be concluded from the diagram? Etended Response. From a lookout tower, Fire is located 9 miles due north and Fire is located miles due east. a. Find the shortest distance firefighters can travel from Fire to Fire. Eplain. A AC DE B AC. DF C DF > BC D DF > AC. Based on the diagram, which is a true statement? A m m B m < m C m > m D GK bisects JGH. b. A campground is located halfwa between the lookout tower and Fire, and another campground is located halfwa between the lookout tower and Fire. Eplain how the answer from part (a) can be used to find the distance between the campgrounds. Then find the distance. c. A fire truck is located in the middle of the shortest path between the two fires. It heads towards the campground located between the lookout tower and Fire. How far must it travel to reach the campground? Eplain. Chapter Assessment Book 97

3 Standardized Test B For use after Chapter Multiple Choice. 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. If RS, RT, ST, WY, WZ, and YZ are all midsegments, find. F A W R Y S Z T 6 H G B C D. Point A is the incenter of nfgh. Find AS. A B C 4 D F R A 6. Given the inscribed circle with center K, which statement can ou not conclude? X M Y O K N A XK YK C NK YZ Z T G H S B NZK > OZK D MK OK. If QS is the perpendicular bisector of PR, find RS. R 7. The point of concurrenc of the three medians of a triangle is called the? of the triangle. A tri-sector point B centrino P (0, ) C median point D centroid A S (, 0) B Ï C Ï D 4. B the Concurrenc of Perpendicular Bisectors Theorem, if QJ, QK, and QL are perpendicular bisectors, then?. A JQK > KQL > LQJ B DE EF FD C QD QE QF D J L E K F 8. If point P is the centroid of nabc, find CP. C (, ) A (6, ) B (0, ) P A B 0 C D 7 9. Which is the longest side of ndef? A DE D E 70 B DF C EF D cannot be determined 80 F D EQK > FQL > DQJ 98 Chapter Assessment Book

4 Standardized Test B continued For use after Chapter 0. Which is a possible value of? Gridded Response A B 4 C 4 D 7 8. R is the centroid of nmnp and JP. Find the perimeter of nmjr. M J 8 N. Using the Hinge Theorem and the diagram, ou can conclude: L R 9 K P K 60 L 0 P Short Response M A m KLM < m QSP B QS LM C PS > LM D none of these. Based on the diagram, which is a true statement? A B 6 E A m A > m D B m A < m D C m A m D D E is the midpoint of BC. C D S 4. In npqr, PQ 0 and PR 9. Write an inequalit to show all possible values for QR. Etended Response. A campground has a convenience store located 00 ards due south of the shower facilities. There is a game room 00 ards 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 laundr half wa between the game room and the convenience store. Find the shortest distance Camper B can travel to get to the pool located half wa 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 Assessment Book 99

5 Standardized Test C For use after Chapter Multiple Choice. Triangle DEF is formed b connecting the midpoints of TABC. The perimeter of TDEF is 4. What is the perimeter of TABC? A B 6 C 48 D 7. In the diagram, HP, MN 6, and MP. Find GK.. Point M is the incenter of TXYZ. Find MC. A B C D 6. Which method could have been used to inscribe the circle inside the triangle? A B 4 C 4 D 8. If UW is the perpendicular bisector of TV, find UV. A Ï B Ï C Ï D Ï 7 4. Which must be true given that C is the circumcenter of TGHK? A CH CK CG B CR CS CT 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 alwas 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 verte of the triangle. D An altitude of a triangle intersects a verte of the triangle. C CH CK D CR RK 00 Chapter Assessment Book

6 Standardized Test C continued For use after Chapter 8. Given that P is the centroid of TABC, find PD. A 0 B 0 C D 0 9. In TPTR, m P and m R 4. Which list gives the sides in order from shortest to longest? A PR, RT, PT C PT, PR, RT B RT, PT, PR D PT, RT, PR Gridded Response. Point A is the centroid of TDEF. Find the perimeter of TADN. Short Response 4. In nstr, ST.6 and TR.. Write an inequalit to show all the possible values for SR. 0. Which can be the measures of the sides of a triangle? A cm, 4 cm, 7 cm B 4 cm, 6 cm, 8 cm C cm, cm, cm D 6 cm, 7 cm, cm. Given that L is the midpoint of JN, which can be concluded from the diagram? A KL, ML B KL. ML C KL ML D KL, LN. B the Hinge Theorem, which inequalit gives the correct restriction on? A, B. C, 9 D. 9 Etended Response. A cargo ship travels due north from a port at a rate of miles per hour while a cruise ship leaves the port at the same time, traveling due east at 0 miles per hour. a. Both ships stop after three hours. What is the shortest distance between the ships? Eplain. b. There is an island 4 miles due north of the cargo ship and another island 60 miles due east of the cruise ship. Eplain how the answer from part (a) can be used to find the shortest distance between the islands. c. A sailboat is equidistant from the two islands and the port. What is the shortest distance between the sailboat and the cargo ship? the sailboat and the port? the sailboat and the cruise ship? Chapter Assessment Book 0

7 Chapter 4, continued illustrates the student s eplanation of when to use the method.. 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. B the Refleive Propert, BD > BD. So, b the HL Congruence Theorem, nabd > ncbd. c. BAD > BCD; ABD > CBD; ADB > CDB; AB > CB ; BD > BD ; AD > CD d. 48 e. C(, ) A(, 0) B(0, 4) E(0, 4) F(, ) D(, 0) f. reflection in -ais g. Sample answer: Use the Distance Formula to find the side lengths of all three triangles. Then use the SSS Congruence Postulate. Chapter Quiz ; Perpendicular Bisector Theorem. 4; Concurrenc of Perpendicular Bisectors Theorem Quiz Quiz. es. No, 4 7 <.. < < 4. 7 < <. BC, AC, AB 6. D, E, F 7. < 8. Chapter Test A (h, 0) 6. h, k RS, RQ, QS 4. B, A, C. es 6. no 7. no 8. < 9. > 0. C, B, A, D Chapter Test B (0, 0), (0, ), (, 0) (0, 0), (0, ), (, ), (, 0) BC, AB, AC 4. QS, QR, RS. 4 < < 6 6. < 7. > 8. Chapter Test C (, ) 9. (, ) Check students drawings 4. BC, AC, AB. G, F, H 6. es; C, A, B 7. no 8. < <. < 9 Standardized Test A. D. B. D 4. C. A 6. B 7. A 8. C 9. A 0. A. D. B CM. and CM, 7. a. B the Pthagorean Theorem, the distance is Ï 9 miles. b. The tower and the fires form a triangle and the shortest distance between the campgrounds is a midsegment of the triangle. It is parallel to the side measuring miles, so its distance is 7. miles. c. 4. miles; The path is the midsegment that is parallel to the side between the tower and Fire, which measures 9 miles. Standardized Test B. B. D. B 4. C. A 6. A 7. D 8. B 9. A 0. B. C. A < QR < 9. a. 4.4 d b. B the Pthagorean Theorem, a b c, so 0 0 c and c < B the Midsegment Theorem, because the pool and laundr room are midpoints, the distance from the laundr room to the pool is half the distance from the game room to the shower. c. Turn clockwise 8 and walk forward 70.7 ards. ANSWERS Assessment Book A9

8 Chapter, continued ANSWERS Standardized Test C. C. D. C 4. A. C 6. B 7. B 8. A 9. D 0. B. A. B ,,.. a. B the Pthagorean Theorem, the distance is Ï 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 0 miles. c. 60 miles; 7 miles; 4 miles SAT/ACT Chapter Test. A. B. E 4. C. D 6. A 7. D 8. A 9. B 0. C. E Performance Assessment. Complete answers should include: an eplanation that a coordinate proof involves placing geometric figures in a coordinate plane; an eplanation that when variables are used to represent the coordinates of a figure in a coordinate proof, the results are true for all figures of the given tpe; an eample of a coordinate proof; an eplanation 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 eample of an indirect proof.. a. (6, 0) and (00, 0) b. units c. No. Because the triangle is obtuse, the circumcenter will lie outside of the rose garden. d. about (70, 0) e. about (0, 0) f. about (77, 0) g. The length of the third side must be less than 7 feet and greater than foot. Chapter 6 Quiz. 6. s. a or Quiz. : , 8 6.,,, 7.,., ø similar; n ABC, ndef 9. not similar 0. similar; npqr, ntsr Quiz Chapter Test A Ï similar; JKLM, PQRS,. similar; ntuv, nxyz, 4 6. similar; nabc, ngfh 7. not similar 8. not similar 9. similar; ndhg, nfhe length 40 m, width 80 m Chapter Test B. : : nabd, necd; AA Similarit Postulate. no in., 4 in in., 6. in.. ft Chapter Test C m LM 8., PQ.0., 89, 44, ø.68, ø.679, 44 ø.68. similar; nabe, ncbd 6. not similar 7. similar; njkl, njmn 8. similar; nehd, nghf A0 Assessment Book