What is a(n); 2. acute angle 2. An angle less than 90 but greater than 0

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1 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 = obtuse angle 4. n angle less than 80 but greater than straight angle 5. n angle = hange 4 to degrees and minutes Given: is a rt. m = Find: m Section.3 8. must be smaller than what number? x 9. must be larger than what number? 4

2 0. an a triangle have sides of length 2, 3, and 26? No < 26 Given: m = 2x + 40 m 2 = 2y + 40 m 3 = x + 2y Find:. m = m 2 = m 3 = 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

3 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 If and, 2. and 3 are in the ratio :2:3, find the measure of each angle. 5, 30, 45 Section One of two complementary angles is twice the other. Find the measures of the angles. 30 and The larger of two supplementary angles exceeds 7 times the smaller by 4. Find the measure of the larger angle. 58 3

4 Section 2.5 Given: GH JK, GH = x + 0 HJ = 8, JK = 2x 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) SSS T S SS S SS 4

5 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 = WV = ST = 52 S W V 5

6 Section 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 = 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, 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

7 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 < 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

8 62. Is b a? Justify your answer. Yes. x = 53/2 and y = 37 b a 2x 37 2x y 3y 2 Section 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

9 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 For and with transversal, 2 and 4 are I. 2 3 If is: 73. 4? ? ? Unknown Unknown Yes Section 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 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

10 80. If f g, find m. 70 f g 8. Given: Name all pairs of angles that must be congruent and 5 Sections is a Find the perimeter of. 2x I x Given: m IPT = 5x 0 KP = 6x Find KT K P T Given: KMOP m M = x 3y m O = x 4 m P = 4y 8 Find: m K K M P O 28 0

11 R 85. Given: RT is a rectangle R = 43x = 24x 742 Find: The length of T to the nearest tenth. 8.7 Sect 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.

12 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 Given: 5 = 70 3 = 30 Find the measures of all the angles. 60, 50, 30, 0, 70, Given: iagram as shown Find: and W = 3 <W = X 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, Given: T = 2x + 6 R RSU = 4x + 6 R = x + 48 Find: m T S 82 T U 20 Sect Given: is the midpoint of Is? If so, by which theorem? Yes, S 2

13 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 What is the sum of the measures of the exterior angles of an octagon? Find the number of diagonals in a 2-sided polygon etermine the number of sides a polygon has if the sum of the interior angles is Sect Find the measure of each exterior angle of a regular 20-gon Find the measure of an angle in a regular nonagon Find the sum of the measures of the angles of a regular polygon if each exterior angle measures Sections 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

14 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

15 _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

16 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

17 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 T Prove: S V V 7

18 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 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

19 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