GEOMETRY SPRING SEMESTER FINALS REVIEW PACKET

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1 NAME DATE PER: GEOMETRY SPRING SEMESTER FINALS REVIEW PACKET For 1 2, use the graph. 6. State the converse of the statement. Then determine whether the converse is true. Eplain. If two angles are vertical angles, then they are congruent. 1. Which segment is congruent to EF? 7. Use the graph. 2. What is the midpoint of GH? Use the following information for 3 4. In the figure, m KJL 32. Write the vector that maps RST to R S T. Use the figure for What is the value of? 4. What is m KJM? 5. Line segment PQ with endpoints P(4, 2) and Q( 2, 0) is rotated 90 clockwise around the origin. What are the coordinates of the midpoint of PQ? 8. How many lines of symmetry does the figure have? 9. What are the angles of rotation less than 360 for the figure? 191

2 Use the following information for In the figures below, ABC LNM. 13. The measures of two complementary angles are represented by the epressions (3 16) and (5 18) Find the value of. 10. What is the value of? 14. Write an equation for the line that passes through (1, 3) and is perpendicular to 1 y What is the value of y? 15. Write an equation for the line that passes through (3, 2) and is parallel to 2 3y In the figure, m In the figure, the measure of 2 is 55. What is m 7? What is the measure of 4? 192

3 17. Use the figures. 21. In the figure, PQ PS. Determine the value of that ensures that the triangles are congruent. For 18-19, state the additional congruency statement or statements needed to prove ABC XYZ for the given theorem. Eplain why PQR PSR. 22. In the figure, m BAC (9 4) and m BAD (3 8). 18. ASA Theorem 19. AAS Theorem 20. Look at the figure below. What value of indicates that AD is the angle bisector of BAC? 23. Use the figure. What is the value of? Are triangles DEF and FGH congruent? Eplain why or why not. If the triangles are congruent, write a congruence statement. 24. The sum of the measures of the interior angles of a regular polygon is 900. How many sides does the polygon have? 193

4 25. Triangle RST is an isosceles triangle with m R 120. What is m S? Eplain your reasoning. 30. In the figure, LP, MP, and NP are perpendicular bisectors. 26. The sides of a triangle measure 5 meters and 8 meters. What are the possible side lengths for the third side? Show your work. If LP 5, LH 12, HP 13, and PM 6, what is PJ? For use the figure. 31. ABCD is a quadrilateral with BE ED and BCD DAB. 27. If EG 4, what is GC? 28. If AF 15, what is AG? If EC 16 cm, m ABC 64, AE 3 5, and m DAB (4y 12), for what values of and y is ABCD a parallelogram? 29.In the figure, MN is the midsegment of JKL. If KM 11 cm and KL 24 cm, what is KN? 194

5 32. State whether each quadrilateral has congruent diagonals. A parallelogram Yes No B rhombus Yes No C rectangle Yes No D isosceles trapezoid Yes No E kite Yes No 33. GIJL is a trapezoid with midsegment HK. 35. A parallelogram has vertices D( 4, 1), E(2, 5), F(4, 3), and G( 2, 3). Determine whether DEFG is a rhombus, rectangle, or neither. Eplain your reasoning. The figure is symmetric about the -ais. If IJ 18 cm and GL 42 cm, what is HK? 34. Triangle PQR is shown in the graph. 36. Find the perimeter of the figure. Round to the nearest tenth. 37. What is the area of the figure? Classify the triangle. Eplain your reasoning. 195

Use the following information for 38-39. Triangle ABC has vertices A( 6, 2), B( 2, 2), and C(4, 8). Dilate ABC using a factor of 1 about the origin.

6 Use the following information for Triangle ABC has vertices A( 6, 2), B( 2, 2), and C(4, 8). Dilate ABC using a factor of 1 about the origin. Then dilate 2 its image using a scale factor of 5 about the origin. 38.Determine the coordinates of the final image. 43. If CD 8, FG 12, and GH 24, what is the length of BC? Use the figure for Determine the scale factor you could use to dilate ABC about the origin that would result in the final image in one step. 40. CDE maps to LMN with the transformation 2 2 (, y) ( 3, y 2), y. 3 3 If CD 9, what is LM? 44. Which triangles are similar? Write a similarity statement. 45.What is AB? 46.Use the figure to find the unknown distance. Use the following information for Polygons BCDE and FGHI are similar. 41. Write a proportion that contains BE and CD. 42. List any angles that are congruent to DEB. What is the distance across the river? 196

7 47. Rectangles ABCD and EFGH are similar. Rectangle ABCD has a length of 20 cm and a perimeter of 60 cm. Rectangle EFGH has a length of 32 cm. Find the area of rectangle EFGH. Use triangle XYZ for Round to the nearest tenth. 52. What is YX? Use the following information for In the figure, PS 4 and SQ 16. Find each length to the nearest tenth. 53. What is YZ? Use the triangle below for questions Round to the nearest tenth. 48.What is the length of RS? 49.What is the length of RP? 54. If m A 50, m B 100, and b 15 cm, what is a? 50.What is the length of RQ? 51.Use the figure. 55.If a 12 cm, b 18 cm, and c 8 cm, what is m A? What is the length of FE? 197

8 56. In the figure, m KJL (12 8) and m KML (10 16). Use the circle for Find the eact arc length of QR. What is the value of? 57 In the circle, mwx 50 and myz Convert the central angle to radians. 62. What is the area of the sector formed by RPQ to the nearest tenth? What is m V? Use the circle for In the circle, mad 38 and mbc Write an equation of a circle with center (3, 4) and radius What is m AED? 59.If DE 3, EB 16, and AE 4, what is EC? 64. Find the center and radius of the circle with the following equation y 4y

9 Use the information for A prism has 6-inch square bases and a height of 10 inches. A cylinder has a diameter of 10 inches and a height of 6 inches. 65. Which solid has the greater volume? 66. Which solid has the greater surface area? 67. The oblique cylinder shown below has a volume of 36 cubic inches. What is the radius of the base of the cylinder to the nearest tenth of an inch? 70.A square pyramid and a cube have equal volumes. The side length of the base of each figure is 16 millimeters. How many times taller is the pyramid than the cube? 71. A cylinder has a radius of 8 inches and a height of 16 inches. The radius of a cone is half the length of the radius of the cylinder. If the cylinder and the cone have equal volumes, how many times greater is the height of the cone than the height of the cylinder? 68. A right cone has a slant length of 9 centimeters and a radius of 4 centimeters. What is the surface area of the cone? Round to the nearest tenth of a square centimeter. Use the following information for A company sells several sizes of the same design of trash cans. The trash cans consist of a cylinder and a hemisphere. The smallest size trash can has the dimensions shown. 69. The triangular prism has a surface area of 510 square meters. Find the missing value for. 72.What is the volume of the trash can to the nearest tenth of a cubic inch? DIAGRAM IS AT TOP OF NEXT COLUMN 199

12 Geometry Name ID: 1 X W2`0i1e8Y kkfuztjar sscopfztkwiazroeu bl\lzcb.t p BAPlnln wrginghh\tmsm qraetsdeprnvkebdo. Date Period For problems 1 and 2, write the equations of the circle in circle standard form by Completing the Square. Identify the center and radius of each. Then sketch the graph. 1) 2 + y y + 13 = 0 2) 2 + y y + 11 = 0 8 y 8 y Use the information provided to write the standard form equation of each circle. 3) Center: (1, 8) Radius: 6 4) Center: (9, 12) Radius: 5 Identify the center and radius of each. Then sketch the graph. 5) ( + 4) 2 + (y - 2) 2 = 4 6) 2 + (y + 2) 2 = 4 8 y y f o2k0w1`8[ lkpurtfae S\oJfPtTwGaBrMea VLLLYCf.Y N PAmlElp Srci[gVhjtnsC Drbe^sPemrZvbeWdp.d q OMHaidbeO AwciQt^hS QIRnUfqiLnoiOt_eM TAhlNgperbhrYau M2F. Worksheet by Kuta Software LLC

13 Geometry Review Sem 2 Final Eam ` 2S0j1e8Y [KDu]t^at bswoffmtrwhaerjev gldl\cg.b s la^lllo hryigg[hctzsq JrKeJsLekrYvZesdT. Circle & Triangles Name ID: 1 Date Period Find the circumference of each circle. Use your calculator's value of p. Round your answer to the nearest tenth. 1) 10.7 yd 2) 9 in Find the area of each sector. Round your answers to the nearest tenth. 3) 4) 60 6 m 13 m 135 Find the length of each arc. Round your answers to the nearest tenth. 5) 6) mi 3 cm 270 Find the missing length indicated. Leave your answer in simplest radical form. 7) 8) f m2b0v1z8l rktujt^ao SjoyfAtwMarreA ql`lscc.h y [AwlQlc rvi]gphltisv RrdeWsfeBrmvuetdV.m ^ pmxahdbeu sweietohu WITnLfmiWnYi[tZeF ^GReGo[myebtqrRyA. -1- Worksheet by Kuta Software LLC

14 9) 9 10) ) 12) Find the area of each. Use your calculator's value of p. Round your answer to the nearest tenth. 13) radius = 3.8 yd 14) diameter = 4 ft Find the circumference of each circle. Use your calculator's value of p. Round your answer to the nearest tenth. 15) diameter = 8 mi 16) diameter = 22 yd A g2r01q8w [KZuHtIaU OSjo^fBtGwgaProen WLLLkCH.X O MAhlAlz LreiKgihstbs\ ZrPe[sleGrqvzeZds.g n WMTaXdhe\ TwAi]tths siangfhianeibteet XGTejokm^eZtircyn. -2- Worksheet by Kuta Software LLC

15 Geometry Sem 2 Final Review Name ID: 1 F z2g0f1k8t \KFuCtuae ps^oofwthwjaer_ey LLpLVCb.G P fallzlg ErcisgphqtRsH Nr^elsWeZrIveeqdM. Law of Sines and Cosines Find each measurement indicated. Round your answers to the nearest tenth. Date Period 1) Find AB A 2) Find BC C 22 km 138 C 24 km B B m A 11.9 m 3) Find m A A 14 yd 4) Find m C 11 ft A B ft C B yd C 5) Find AB C 6) Find AB A 28 km mi A 43 B C B 7) Find m A 31 km A 8) Find m A A B 7 cm cm C C km B f B2`0h1b8H QKJuntFaP XSMoSfStEw_awrUeE [LiLRCG.q \ haulklt zr_ing\htlsl vrrems`edrhvieydv. c ympawdney zwkietahr qiengfoianciwtiem OAVlCgse^bvr^aT F2_. Worksheet by Kuta Software LLC

16 Geometry- Final Review Sem 2 S k2a0v1d8v OKuuMtraj lsmoyfzt`wqaurjeo ]LjLYCF.N G camlmlr Wr[iYghmtWss jrwels^efrzvsemdq. Probability, Permutations, Combinations Find the number of possibilities in each scenario. 1) A team of 14 softball players needs to choose a captain and co-captain. 2) Selecting which eight players will be in the batting order on a 11 person team. 3) Mark has homework assignments in si subjects. He only has time to do three of them. 4) There are 15 applicants for four jobs: Computer Programmer, Software Tester, Manager, and Systems Engineer. Find the number of possible outcomes in the sample space. 5) A coffee shop offers small, medium, and large sizes. Customers can choose between French roast and Italian roast. 6) There is one quarter, one dime, and one nickel in your pocket. You randomly pick a coin from your pocket and place it on the counter. Then you pick a second coin from your pocket. Find the number of unique permutations of the letters in each word. 7) SLIGHTLY 8) CONNECT Find the probability of each event. 9) Molly is carrying eight pages of math homework and three pages of English homework. A gust of wind blows the pages out of her hands and she is only able to recover eight random pages. What is the probability that she recovers all of her math homework? 10) A car dealership has nine cars in the lot. Unfortunately, the keys to the cars have been mied up. The manager randomly grabs a key and tries to start a car. A salesman also randomly picks a different key and tries to start another car. What is the probability that both cars start? F J2X0S1n8p ikiuutiar RSjoDftCwqakrte_ ELoLuC.u e OAHl_lT mrvi^gohstgse bryetsnejrbvqendm.w s pmxa]diee nwfi\tuh PIpnifriMn_ietgei ga_logjeqbvruae R2Q. Worksheet by Kuta Software LLC

GEOMETRY SPRING SEMESTER FINALS REVIEW PACKET

Name Date Class GEOMETRY SPRING SEMESTER FINALS REVIEW PACKET For 1 2, use the graph. 6. State the converse of the statement. Then determine whether the converse is true. Explain. If two angles are vertical