Study Guide for Final Exam Honors Geometry 1. Explain what is ...

Study Guide for Final ExamHonors Geometry1. Explain what is meant by a rigid transformation. point O. Find the image of RS .2. Is the transformation below an isometry?Explain.AB3. The reflection image of MN in line q is .RQOSTDADCCBNML10. State whether the following figure hasreflectional symmetry, rotational symmetry, bothkinds of symmetry, or neither kind of symmetry.qO4. The points in a coordinate plane are reflected inthe y-axis. In general, every point (x, y) is mappedonto what point?5. The points in a coordinate plane are reflected inthe line y = x. In general, every point (x, y) ismapped onto what point?6. Which of the following letters (if drawn assimply as possible) has at least one line ofsymmetry?Q, R, W, N11. Segment AB is translated by the motion rule (x,y) → (x – 4, y + 5).Find the coordinates of theendpoints of the image A′ B′.[A] W[B] R[C] N[D] Q7. How many lines of symmetry does an isoscelesright triangle have? Draw a diagram to illustrate.8. Sketch, if possible, an isosceles trapezoid withexactly two lines of symmetry.9. Rectangle QRST is rotated 90° clockwise about12. Explain whether or not the composition of twoor more isometries is an isometry.13. Explain whether or not, in a composition of twoor more isometries, the order of applying themmatters.14. Write the ratio of the value of 2 pennies to thevalue of 2 dimes.

Study Guide for Final ExamHonors Geometry5 7∆ ABC ′′ ′′ ′′ A. What is the relationship between15. Solve the proportion = .x – 1 x∆ ABC and ∆ ABC ′′ ′′ ′′ ?B. Find the values of x andy to the nearest tenth.C. Are the values determined16. Consider the proportion R S= . If thefor x and y unique?W Tproduct of the means increases, what must happento the product of the extremes? Explain yourreasoning.17. Given that a c= , decide whether it is true orb dnot that a b= . Explain your reasoning.c d18. Are the two triangles (not drawn to scale)similar? If so, explain why they are.23. If p || q, solve for x.14 2021 xp1603677° 13°164q24. In the figure shown, BC || DE , AB = 8 yards,BC = 9 yards, AE = 14 yards, and DE = 18 yards.Find CE .13°4177°A409BC19. Are all regular hexagons similar? Explain.20. If possible, draw two isosceles triangles inwhich all the sides of equal length in both trianglesare congruent, but the two triangles are not similar.21. Given that ∆ ABC ∼ ∆ DEF, solve for x and y.AyB9D4xC E5 3FD25. State the postulate or theorem that can be usedto prove that the two triangles aresimilar.26. Given AE || BD . Solve for x.E22. Given: ∆ ABC ~ ∆ ABC ′ ′ ′, ∆ ABC ′ ′ ′ ~

Study Guide for Final ExamHonors GeometryAxB132826aE5D10C32. Which of the following sets are Pythagoreantriples?A. 3 , 4 , 5 B. 12, 16, 20C. 1 3 , 1 4 , 1 5 D.27. Give the scale factor for the dilation of thesquare shown.A′ B′A7.54.5B3 2 , 4 2 , 5233. Choose the sets that are possible side lengths ofa right triangle.A. 1, 1, 2B. 1, 1, 2 C. 3, 4, 7D. 3,4, 5D′DCC′34. For each set of numbers, determine whether thenumbers represent the lengths of the sides of anacute triangle, a right triangle, an obtuse triangle, orno triangle.A. 34, 29,7B. 8, 15, 17C. 7.1, 10.8, 23.328. Find the scale factor to two decimal places forthe dilation shownbelow.3830C35. Find the value of x and y .x46P'P45° 30°y36. Find sin P, cos P, tan P.29. Find a, b, and h.ahb4 1230. Find the geometric mean of 6 and 24.31. Find the length of the leg of this right triangle.Give an approximation to 3 decimal places.202129P37. Use a calculator to find cos 17°, cos 37°, cos57°, and cos 77°. As the angle increases, whathappens to the cosine of the angle? Explain.38. A slide 4.1 m long makes an angle of 28 ° withthe ground. How high is the top of the slide abovethe ground?

Study Guide for Final ExamHonors GeometryFind the length of the radius r, to the nearest tenth.39. Find the value of x, to the nearest wholenumber. (not drawn to scale)A 9 BG53° 15r4IxHO40. Find x, to the nearest hundredth.1847. Given: OA is tangent to Q at AList any right angles. Explain.x42°48. Given: In O, m BAC = 298 ° . Find m ∠ BOC.41. Solve the right triangle: α = 30° and a = 18;find β , b, and cOCcαbBβaA42. Define a chord of a circle.43. Define a diameter of a circle.44. Define a secant of a circle and illustrate thedefinition on the circle below.49. Identify the minor congruent arcs in the figure.DC70°B35°45°25° 70°60°55°AG45. Draw a common external tangent to P andQ, on the figure below.EF50. Find the value of x.46. AB is tangent to O at A (not drawn to scale).

Study Guide for Final ExamHonors GeometryPQ143xSR51. Find RS in C. Explain yourreasoning.55. Given: G with intersecting chords AB andCD that meet at P. Can triangles ∆ADP and∆CBP be congruent? Can they be similar? Canthey be neither congruent nor similar?Explain.52. Given: P and PT ⊥ to chord RS at T. Decidewhether or not RT = TS. Explain yourreasoning.56. What must be the measures of ∠ C and ∠ D sothat a circle may be circumscribed about ABCDbelow?53. Given: Diameters PV and RT in Q. Decidewhether or not PT ≅ RV .Explain yourreasoning.54. Find m ∠ PSQ if m ∠ PSQ = 2y −10andm ∠ PRQ = y + 35 .57. In the figure shown (not drawn to scale),mBCD = 117° , mDEF = 92° , mFGH = 133° ,and mHAB = 18°. Find m ∠ FPD .C•D•• EB•• AP • ••HF•G) )58. Find the value of x if m AB = 68° and m CD

= 35° (not drawn to scale).Study Guide for Final ExamHonors Geometrynearest tenth.A x°ODC4•5•?•12••B59. Find the value of x.91022x62. Write the standard equation of the circle withcenter (–3, 5) and radius 5 2 .63. Describe the locus of the tip of a pendulum as itswings.64. Sketch and describe the locus of all points in aplane that are 2 centimeters from a circle with aradius of 6 centimeters.65. Sketch and describe the locus of all points in aplane that are equidistant from the points on acircle.60. Find the diameter of the circle. BC = 12, andDC = 19. Round your answer to the nearest tenth.AOBDC61. Find the length of the missing segment to the66. Find the sum of the measures of the interiorangles of a decagon.67. A regular pentagon has five congruent interiorangles. What is the measure of each angle?68. Find the area of an equilateral triangle with side12.69. The perimeter of an equilateral triangle is 18.Find its area.70. Find the area of a regular nonagon with side 10cm.271. The area of a regular octagon is 50 cm . Whatis the area of a regular octagon with sides threetimes as large as the sides of the first octagon?

Study Guide for Final ExamHonors Geometry79. Find the surface area of the right prism below.72. Find the circumference of a circle with radius 8mm. Use π ≈ 314 . .73. A circle has a circumference of 32 meters. Findits radius.74. The circumference of a circle is 68π cm. Findthe diameter, the radius, and the length of an arc of110°.75. The figure below represents the overhead viewof a deck surrounding a hot tub. What is the area ofthe deck? Use π ≈ 314 . .80. Calculate the surface area of a cylindrical watertank that is 6 m high and has a diameter of 8m.Use π ≈ 314 . .81. The figure shown below is a cylindrical solidwith a circular cylindrical hole drilled out of thecenter. Find the surface area of the resulting solid.1.7 m4 m76. Find the area of the shaded region. (Assume thatthe ends of the figure are semicircles.)82. The pyramid below has a square base and aslant height of 7 ft. Find its surfacearea.77. Find the number of vertices, faces, and edges forthe figure.83. Find the surface area of the right cone below.(Round the result to two decimalplaces.)84. Find the volume of the rectangular prism.1 m78. A polyhedron has 9 faces and 21 edges. Howmany vertices does it have? Explain your answer.6 m5 m

Study Guide for Final ExamHonors Geometry85. Which has a greater volume: a cube of edge terms of π .length x or a cylinder with height of x and diameterof x? Explain.92. Find the volume of a sphere 6 ft in diameter.Use π ≈ 314 . and round your answer to the nearest86. Find the volume of a cylinder with height 8.6 m tenth.and diameter 4 m. Use π ≈ 314 . .93. The areas of corresponding faces of two similar87. Find the volume of the right triangular prism. triangular prisms are 49 cm 2 and 36 cm 2 . What isthe ratio of the corresponding side lengths? of theperimeters of the corresponding faces? of thevolumes?4 m11 m7 m[A] 39 m 3[B] 308 m 3[C] 154 m 3[D] 25 m 388. Find the volume of the cylinder below. (Roundthe result to one decimalplace.)89. Calculate the volume of a cone with height 8feet and radius 3 feet.90. Find the diameter of a sphere that has a surfacearea of 144 . π in 291. Find the surface area of a sphere that has adiameter of 18 centimeters. Express your answer in

Reference: [7.1.1.4][1] Every image is congruent to its preimage.Study Guide for Final ExamHonors Geometryoverall composition preserves length and is anisometry.Reference: [7.1.1.5][2] No. It is not a rigid transformation.Reference: [7.2.1.12][3] ABReference: [7.2.1.16][4] (–x, y)Reference: [7.2.1.17][5] (y, x)Reference: [7.2.2.31][6] [A]Reference: [7.2.2.37][7] 1; diagrams vary.Reference: [7.2.2.38][8] Not possible.Reference: [7.3.1.41][9] BCReference: [7.5.2.84][13] For many compositions, different results areobtained when the order is altered. Each case mustbe examined individually.Reference: [8.1.1.2][14] 1:10Reference: [8.1.2.15][15] x = 7 2Reference: [8.1.2.18][16] The product of the extremes must also increasebecause the two products must remain equal inorder for it to be a proportion.Reference: [8.2.1.32][17] It is true. Both proportions have the same crossproducts: ad = bc.Reference: [8.3.1.36][18] Yes; corresponding angles are equal inmeasure and ratios of corresponding sides are allequal.Reference: [7.3.2.50][10] reflectionalReference: [7.4.1.57][11] A´(–3, 10); B´(1, 2)Reference: [7.5.2.82][12] Since each isometry preserves length, theReference: [8.3.1.40][19] Yes. Since all regular hexagons are bothequiangular and equilateral, their correspondingangles must be congruent and the lengths ofcorresponding sides must be proportional.Reference: [8.3.1.43]

[20] Sketches vary; for example,Study Guide for Final ExamHonors Geometry[30] 12Reference: [8.3.1.47][21] x = 5.4, y = 6.67Reference: [8.3.1.51][22] A. ∆ ABC ~ ∆ ABC ′′ ′′ ′′ B. x ≈ 6.6; y ≈ 43.7C.YesReference: [8.4.1.63][23] 30Reference: [8.4.1.64][24] 7 ydReference: [8.5.1.74][25] AA Similarity PostulateReference: [8.6.1.82]Reference: [9.2.2.9][31] 10.392Reference: [9.2.2.24][32] BReference: [9.3.1.27][33] B and DReference: [9.3.2.30][34] A. acute triangle, B. right triangle, C. notriangleReference: [9.4.1.41][35] x = 23 2, y = 23 + 23 3 or 23(1 + 3 )Reference: [9.5.1.62]20 21[36] sin P = , cos P = , tan P =29 292021[26] 6 1 2Reference: [8.7.1.96][27] 5 3Reference: [9.5.1.69][37] ≈ 0.956, ≈ 0.799, ≈ 0.545, ≈ 0.225;decreases, the ratio of the adjacent side to thehypotenuse becomes smaller.Reference: [8.7.1.99][28] 2.27Reference: [9.1.2.2][29] a = 8, b = 8 3, h = 4 3Reference: [9.1.2.7]Reference: [9.5.2.74][38] 1.92 mReference: [9.6.1.77][39] 12Reference: [9.6.1.78][40] 13.38

Reference: [9.6.1.83][41] β = 60°b ≈ 3118 .c ≈ 36.00Study Guide for Final ExamHonors GeometryCD ≅ EF; BG ≅ FD ≅ EC; BF ≅ GD ≅ DA;AF ≅ DB; CG ≅ EBReference: [10.2.2.39a][50]Reference: [10.1.1.3][42] A chord of a circle is a segment with endpointson the circle.Reference: [10.2.2.42][51] RS = 7. In a circle, two chords that areequidistant from the center are congruent (Theorem10.7).Reference: [10.1.1.4][43] A diameter is a chord that passes through thecenter of a circle.Reference: [10.1.1.12][44] A secant of a circle is a line that intersects acircle twice. Sketches vary. For example,Reference: [10.1.1.11][45] Two possible answers.Reference: [10.1.2.19][46] 8.1Reference: [10.1.2.22][47] ∠QAO . If a line is tangent to a , then it is ⊥to the radius drawn to the point of tangency; twolines are ⊥ if they intersect to form a right ∠ .Reference: [10.2.1.31a][48]Reference: [10.2.1.37][49]Reference: [10.2.2.43][52] Yes, RT = TS. A diameter that is perpendicularto a chord bisects the chord and its arc (Theorem10.5).Reference: [10.2.2.45][53] PT ≅ RV . ∠PQT≅∠RQV by the VerticalAngles Theorem, so PT ≅ RV ; then PT ≅ RVbecause, in the same circle, congruent minor arcshave congruent chords (Theorem 10.4).Reference: [10.3.1.50a][54]Reference: [10.3.1.54][55] (Answers may vary.) They are congruent ifAD ≅ CB but similar ) otherwise. ∠A≅ ∠C sincethey both intercept DB , and ∠D≅ ∠B since they)both intercept AC . Therefore, ∆ADP ~ ∆CBP bythe AA Similarity Postulate. If AD ≅ CB, ∆ADP≅ ∆CBP by the ASA Congruence Postulate.Reference: [10.3.2.58][56] m ∠ C = 100°, m ∠ D = 70°Reference: [10.4.2.66][57] 37 °

Study Guide for Final ExamHonors GeometryReference: [10.4.2.72][58] 51.5°Reference: [11.1.1.1][66] 1440 °Reference: [10.5.1.78][59] 24 4 9Reference: [11.1.1.4][67] 108 °Reference: [10.5.2.79a][60]Reference: [11.2.1.18][68] 36 3 sq. unitsReference: [10.5.2.80][61] 17.3Reference: [10.6.1.85]2 2[62] ( x+ 3) + ( y–5) =254Reference: [11.2.1.22][69] 9 3 sq. unitsReference: [11.2.2.23][70] 618.2 cm 2Reference: [10.7.1.92][63] The arc of a circle.Reference: [11.3.1.33a][71]Reference: [10.7.1.95][64] Two circles; one with radius 4 cm, anotherwith radius 8 cm.Reference: [11.4.1.39][72] 50.24 mmReference: [11.4.1.41a][73]4 2 2Reference: [11.4.1.45][74] 68 cm; 34 cm; 20.78π cmReference: [11.5.2.66]2[75] 30. 4266 mReference: [10.7.1.97][65] A single point; the center of the circle.Reference: [11.5.2.72][76] ≈ 322 sq. units

Reference: [12.1.1.1][77] 7 vertices, 7 faces, 12 edgesStudy Guide for Final ExamHonors GeometryReference: [12.4.2.44][88] 189. 65625π ft ≈ 5958 . ft3 3Reference: [12.1.2.10][78] 14, because F + V = E + 2 and 9 + 14 = 21 + 2.Reference: [12.5.1.54][89] 24π f t 3Reference: [12.2.1.16][79] 54 in. 2Reference: [12.6.1.62][90] 12 in.Reference: [12.2.2.19]2[80] 2512 . mReference: [12.6.1.63][91] 324 π c m 2Reference: [12.2.2.20][81] 24 π in. ≈ 754 . in.2 2Reference: [12.6.2.70][92] 113 ft 3Reference: [12.3.1.27][82] 95 ft 2Reference: [12.7.1.78][93] 7:6; 7:6; 343:216Reference: [12.3.2.30][83] 123 . 75π cm ≈ 388.77 cm2 2Reference: [12.4.1.34]3[84] 30 mReference: [12.4.2.40][85] The cube; the cube has volume of x 3 while thecylinder has volume of π x4≈ 079 . x .3 3Reference: [12.4.2.41][86] 108.02 m 3Reference: [12.4.2.42][87] [C]