Geometry Review Packet Semester Final Name Section.. Name all the ways you can name the following ray:., Section.2 What is a(n); 2. acute angle 2. n angle less than 90 but greater than 0 3. right angle 3. n angle = 90 4. obtuse angle 4. n angle less than 80 but greater than 90 5. straight angle 5. n angle = 80 2 6. hange 4 to degrees and minutes. 5 4 24 7. Given: is a rt. m = 67 2 37 Find: m 22 38 23 Section.3 8. must be smaller than what number? 6 0 6 x 9. must be larger than what number? 4
0. an a triangle have sides of length 2, 3, and 26? No 2 + 3 < 26 Given: m = 2x + 40 m 2 = 2y + 40 m 3 = x + 2y Find:. m = 80 2. m 2 = 00 3. m 3 = 80 2 3 4. H is divided by F and G in the ratio of 5:3:2 from left to right. If H = 30, find FG and name the midpoint of H. FG = 9 F is the midpoint Section.4 Graph the image of quadrilateral SKH under the following transformations: 5. Reflect across the y-axis 6. Then reflect across the x-axis Section.7 7. What is a postulate? n idea that can t be disproven so is accepted as true. 8. What is a definition? n accepted meaning of a word or phrase. 9. What is a theorem? n idea that is provable. 2
20. Which of the above (#7-9) are reversible? efinitions Section.8 2. If a conditional statement is true, then what other statement is also true? ontrapositive State the converse, inverse, and contrapositive for the following conditional statement: If heryl is a member of the Perry basketball team, then she is a student at Perry. 22. onverse: If heryl is a student at Perry, then she is a member of the Perry basketball team. 23. Inverse: If heryl is not a member of the Perry basketball team, then she is not a student at Perry. 24. ontrapositive: If heryl is not a student at Perry, then she is not a member of the Perry basketball team. 25. Place the following statements in order, showing a proper chain of reasoning. Then write a concluding statement based upon the following information: a b d => f or ~f => ~c d ~c ~c a b f Section 2. 26. If and, 2. and 3 are in the ratio :2:3, find the measure of each angle. 5, 30, 45 Section 2.2 2 3 27. One of two complementary angles is twice the other. Find the measures of the angles. 30 and 60 28. The larger of two supplementary angles exceeds 7 times the smaller by 4. Find the measure of the larger angle. 58 3
Section 2.5 Given: GH JK, GH = x + 0 HJ = 8, JK = 2x - 4 29. Find: GJ 32 Section 2.6 G N 30. Given: HGJ ONP GJ and NP are bisectors m HGJ = 25, m ONR = (2x + 0) Find: x H J K O P R 20 Section 2.8 (3x + 42) 3. Is this possible? Yes, x = -3 (4x + 45) Section 3.2 Name the method (if any) of proving the triangles congruent. (SSS, S, SS, S, HL) 3. 32. SSS T 33. 34. S SS 35. 36. S SS 4
37. 38. HL T 2. Identify the additional information needed to support the method for proving the triangles congruent. K O G HGJ OMK 39. by SS OK = HJ M 40. by S <G = <M H J 4. by HL KM = GJ V PSV TRV 42. by SS PS = TR 43. by S <SVP = <TVR 44. by S <VSP = <VRT P R S T W Z ZW XY 45. by SSS W = Y or W = Y 46. by SS <ZW = <XY X Y Section 3.4 T Given: TW is a median ST = x + 40 SW = 2x + 30 WV = 5x 6 Find: 47. SW = 54 48. WV = 54 49. ST = 52 S W V 5
Section 3.6 50. If the perimeter of ΔFG is 32, is ΔFG scalene, isosceles, or equilateral? 0 G x + 7 Scalene x = 6 2x - 3 F 5. Given: and are the legs of isosceles Δ. m = 5x m 3 = 2x + 2 Find: m 2 x = 24 60 3 2 52. If the m is acute, what are the restrictions on x? x < 70 and x > -20 (x + 20) 53. Given: m, m 2, m 3 are in the ratio 6:5:4. Find the measure of each angle. 72, 60, 48 2 3 54. If ΔHIK is equilateral, what are the values of x and y? H x = 7 y = 63 5 x + 8 I 3 y 6 K 6
Section 3.7 Q 55. Given: m P + m R < 80 PQ < QR Write an inequality describing the restrictions on x. P (7x 8) (4x) R 6 < x < 8 56. Given: Solve for x. x = -5 or (x 2 6x) 55 Section 4. Find the coordinates of the midpoint of each side of. 57. Midpoint of = (,4) (-4, 3) (6, 5) 58. Midpoint of = (6,2) 59. Midpoint of = (,) (6, -) 60. Find the coordinates of, a point on circle O. (8,0) (x, y) O (7, 6) Section 4.3 (6, 2) 6. If squares and are folded across the dotted segments onto, find the area of that will not be covered by either square. 8 8 sq units 4 7
62. Is b a? Justify your answer. Yes. x = 53/2 and y = 37 b a 2x 37 2x y 3y 2 Section 4.6 63. has a slope of 2 5. If = (2, 7) and = (2, c), what is the value of c? c = 32 Use slopes to justify your answers to the following questions. 64. Is R T? (9, 8) Yes T (-3, 4) 65. Is TR? (0, 5) Yes 66. Show that R is a right angle. R (-2, ) TR = -3 R = /3 Given the diagram as marked, with an altitude and a median, find the slope of each line. 67. = /4 (5, 9) 68. = -4 (, 3) 69. = -7/2 (3, ) 70. line through and parallel to. /4 8
Section 5. Use the diagram on the right for #7-75. Identify each of the following pairs of angles as alternate interior, alternate exterior, or corresponding. 7. For and with transversal, and are orresponding. 4 5 72. For and with transversal, 2 and 4 are I. 2 3 If is: 73. 4? 74. 4 3? 75. 4 2? Unknown Unknown Yes Section 5.2 76. If 2, which lines are parallel? Q R PQ and RS P 2 S 77. Write an inequality stating the restrictions on x. -47 < x < 30 x 50 3 Section 5.3 78. re e and f parallel? 2x 0 e No x = 25 3x 30 5x 20 f 79. Given: a b m = x 3y m 2 = 2x 30 m 3 = 5y 20 Find: m 70 a 2 b 3 9
80. If f g, find m. 70 f 50 00 g 8. Given: Name all pairs of angles that must be congruent. 2 3 4 2 and 5 Sections 5.4 5.7 6 5 82. is a Find the perimeter of. 2x + 6 36 8 I x + 8 83. Given: m IPT = 5x 0 KP = 6x Find KT K P T 240 84. Given: KMOP m M = x 3y m O = x 4 m P = 4y 8 Find: m K K M P O 28 0
R 85. Given: RT is a rectangle R = 43x = 24x 742 Find: The length of T to the nearest tenth. 8.7 Sect. 6.-6.2 T 86. a b = GY 87. T and point R or O determine plane b. 88. M, and T determine plane a a G Y O M T b 89. T and GM determine plane a R 90. Name the foot of OR in a. Y 9. Is M on plane b? No W 92. Given: WY XY WYZ = 3 x + 68 WYX = 2x 30 a Is WY a? No x = 60 X Y Z Sect. 6.3 n 93. Is a plane figure? Yes 94. If m n, is? Yes 95. If, is m n? No m True or False. 96. F Two lines must either intersect or be parallel. 97. T In a plane, two lines to the same line must be parallel. 98. F In space, two lines to the same line are parallel.
99. T If a line is to a plane, it is to all lines on the plane. 00. F Two planes can intersect at a point. 0. F If a line is to a line in a plane, it is to the plane. 02. F If two lines are to the same line, they are parallel. 03. T triangle is a plane figure. 04. T Three parallel lines must be co-planar. 05. T very four-sided figure is a plane figure. Sect 7. 06. Given: 5 = 70 3 = 30 Find the measures of all the angles. 60, 50, 30, 0, 70, 70 07. Given: iagram as shown Find: and W = 3 <W = 60 2 3 X 40 80 5 6 4 08. Find the restrictions on x. W 26 Y -3 < X < 27 (4x + 2) 09. The measures of the 3 s of a are in the ratio 2:3:5. Find the measure of each angle. 36, 54, 90 0. Given: T = 2x + 6 R RSU = 4x + 6 R = x + 48 Find: m T S 82 T U 20 Sect. 7.2. Given: is the midpoint of Is? If so, by which theorem? Yes, S 2
2. If I, is IF NL? If so, by which theorem? No hoice Theorem I N Sect. 7.3 F L 3. Find the sum of the measures of the angles in a 4-gon. 260 4. What is the sum of the measures of the exterior angles of an octagon? 360 5. Find the number of diagonals in a 2-sided polygon. 54 6. etermine the number of sides a polygon has if the sum of the interior angles is 2340. 5 Sect 7.4 7. Find the measure of each exterior angle of a regular 20-gon. 8 8. Find the measure of an angle in a regular nonagon. 40 9. Find the sum of the measures of the angles of a regular polygon if each exterior angle measures 30. 800 Sections. - 7.4 Sometimes, lways or Never (S,, or N) S_ 20. The triangles are congruent if two sides and an angle of one are congruent to the corresponding parts of the other. 2. If two sides of a right triangle are congruent to the corresponding parts of another right triangle, the triangles are congruent. _N* 22. ll three altitudes of a triangle fall outside the triangle. _N 23. right triangle is congruent to an obtuse triangle. _ S 24. If a triangle is obtuse, it is isosceles. _N 25. The bisector of the vertex angle of a scalene triangle is perpendicular to the base. 26. The acute angles of a right triangle are complementary. 3
27. The supplement of one of the angles of a triangle is equal in measure to the sum of the other two angles of the triangle. _N 28. triangle contains two obtuse angles. 29. triangle is a plane figure. _S 30. Supplements of complementary angles are congruent. 3. If one of the angles of an isosceles triangle is 60, the triangle is equilateral. N_ 32. If the sides of one triangle are doubled to form another triangle, each angle of the second triangle is twice as large as the corresponding angle of the first triangle. _S 33. If the diagonals of a quadrilateral are congruent, the quadrilateral is an isosceles trapezoid. 34. If the diagonals of a quadrilateral divide each angle into two 45-degree angles, the quadrilateral is a square. _S 35. If a parallelogram is equilateral, it is equiangular. _S 36. If two of the angles of a trapezoid are congruent, the trapezoid is isosceles. 37. square is a rhombus _S 38. rhombus is a square. 39. kite is a parallelogram. 40. rectangle is a polygon. 4. polygon has the same number of vertices as sides. _N 42. parallelogram has three diagonals. _N 43. trapezoid has three bases. _S 44. quadrilateral is a parallelogram if the diagonals are congruent. _S 45. quadrilateral is a parallelogram if one pair of opposite sides is congruent and one pair of opposite sides is parallel. 46. quadrilateral is a parallelogram if each pair of consecutive angles is supplementary. 47. quadrilateral is a parallelogram if all angles are right angles. 4
_S 48. If one of the diagonals of a quadrilateral is the perpendicular bisector of the other, the quadrilateral is a kite. 49. Two parallel lines determine a plane. _N 50. If a plane contains one of two skew lines, it contains the other. 5. If a line and a plane never meet, they are parallel. _S 52. If two parallel lines lie in different planes, the planes are parallel. 53. If a line is perpendicular to two planes, the planes are parallel. 54. If a plane and a line not in the plane are each perpendicular to the same line, then they are parallel to each other. 55. In a plane, two lines perpendicular to the same line are parallel. _S 56. In space, two lines perpendicular to the same line are parallel. 57. If a line is perpendicular to a plane, it is perpendicular to every line in the plane. _S 58. If a line is perpendicular to a line in a plane, it is perpendicular to the plane. _S 59. Two lines perpendicular to the same line are parallel. 60. Three parallel lines are coplanar. Geometry Final Proof Review 6. Given: Prove: is a rectangle 62. Given: m m is isosceles, with base Prove: 5
63. Given: is an altitude F is an altitude is a parallelogram Prove: F F 64. Given: Prove: 65. Given: is an altitude Prove: is a median a 66. Given: G is a rectangle,, F & H are midpoints Prove: HF is a parallelogram H G F 6
67. Given: O, O is an altitude Prove: O 68. Given: <F <F F Prove: 69. Given: is isosceles with base,, F are midpoints F Prove: F S 70. Given: is complementary to 4 2 is complementary to 3 RT bisects SRV R 3 4 2 T Prove: S V V 7
7. Given: is isosceles with base F G, FH, GI OFG OGF Prove: HFO IGO F G H O I 72. Given: iagram as shown 2 3 4 4 Prove: 2 3 R T S 73. Given: OP RS KO KS M is the midpoint of OK T is the midpoint of KS M K T Prove: MP TR O P R S 74. Given: PR ST NP VT P T Prove: WRS is isosceles P T W N S R V 8
75. Given: XYZ is isosceles with base YZ X, trisect YZ Prove: X X Y Z 76. Given: P is the midpoint of XZ Z 2 Prove: XY YZ W Y P 2 X 77. Given: F F F F Prove: is a parallelogram 9