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1 1. Match each vocabulary word to the picture. A. Linear Pair B. Vertical Angles P1 C. Angle Bisector D. Parallel Lines E. Orthocenter F. Centroid For questions 3 4 use the diagram below. Y Z X U W V A B 3. Name all possible lines on the given figure. P3 C E D 4. Name all possible rays on the given figure. 5. AC = 72 BC = A B 2x + 3 5x - 8 P4 E A B C C D 6. Solve for x. (3x + 10) (2x + 15) P5 P 7. C (6x 125) T P6 A C B D 2. Name all the possible segments on AD. A B C D Find B m CAB A (2x + 39)!!!" 8. AB bisects CAT. If m CAT = 30 and m CAB = 2x + 10 then give the value of x.!!!" 9. AB bisects CAT. If m CAT = 8x 30 and m CAB = 2x + 10 then give the value of x. M Revised 2015 Geometry Honors Semester 1 Review Page 1 of 16

2 !!!" 10. AB bisects CAT. If m BAT = 5x + 20 and m CAB = 2x + 50 then give the measure of CAT. 11. Choose the terms below that can be defined. line space parallel segment point ray plane Use the diagram below for questions If AB has endpoints A(2, -1) and B(10, 13) then give the midpoint of AB. 18. In the diagram above, m 1= ( 5x + 20 ) and m 2 = ( 3x + 16 ). What is m 2? A. 18 B. 2 C. 22 D If AB has endpoint A(2, 13) and midpoint (10, -1) then give the coordinates of B. 19. In the diagram above, m 1= ( 5x 20 ) and m 2 = ( 3x + 8 ). What is m 1? 14. What is the distance between (-5, 2) and (-9, -4)? Given: Δ ABC is isosceles with AB = BC. If m A = 30 then find the m B. 16. Given: ΔRST is isosceles with RS = ST. If m R = 40 then find m S. 17. Given: ΔRST is isosceles with TS = RT. If m R = 40 then find m S. True or False (A through E): A. Angles 1 and 11 are corresponding angles. B. Angles 7 and 5 are corresponding angles. C. Since no lines have been said to be parallel, there are no corresponding angles in this picture. D. Angles 5 and 10 are alternate interior angles. E. Angles 14 and 11 are alternate interior angles. Revised 2015 Geometry Honors Semester 1 Review Page 2 of 16

3 21. Find the value of x and y in the diagram below, if the lines p and q are parallel. 23. ΔCAR is isosceles with CA = RA. If m CRD = 105 then fill in the angle measures below. x = A B. 20 R. m CAT S. m BAT T. m BAR U. m CAR C. 2.9 D. 4 y= A. 30 B C. 11 D If m AEB = (2x + 32) and 1 m DEC = x + 65, what is the 2 value of x? A C E B A D 24. Which are congruent? (Check ü ) A. Base angles of an isosceles triangle B. Corresponding angles of parallel lines C. Diagonals of a rectangle D. Diagonals of an isosceles trapezoid E. Vertical angles F. Linear pairs G. Alternate interior angles of parallel lines H. Opposite angles of a parallelogram I. Consecutive angles of a parallelogram 25. Which of the following are supplementary? (Check ü ) A. Base angles of an isosceles triangle B. Corresponding angles of parallel lines C. Diagonals of a rectangle D. Diagonals of an isosceles trapezoid E. Vertical angles F. Linear pairs G. Alternate interior angles of parallel lines H. Opposite angles of a parallelogram I. Consecutive angles of a parallelogram Revised 2015 Geometry Honors Semester 1 Review Page 3 of 16

4 26. Consider the following statement: For two real numbers a and b, if a < b, then a 2 < b 2. Select ALL that can be used to prove that the statement is sometimes false? A. a = -4 and b = 3 B. a = 4 and b = 5 C. a = -6 and b = 4 D. a = -1 and b = Fill out the reasons for the algebraic proof: Given: 5(x + 2) 4 = 21 Prove: x = 3 Statements Reasons 1. 5(x + 2) 4 = (x + 2) = x + 10 = x = x = Which is the converse of the statement If a triangle has all acute angles then it is an acute triangle.? A. If a triangle has all acute angles, then it is an acute triangle. B. If a triangle is an acute triangle then it has all acute angles. C. If a triangle does not have all acute angles then it is not an acute triangle. D. If a triangle is not an acute triangle then it does not have all acute angles. 29. Name the corresponding congruent parts of the following triangles. 30. What is the value of y? 31. What is the value of m TRI? 32. Given R Tand RSU TUS. We know RUS TSU by? A. SSS B. SAS C. AAS D. ASA 33. If AB bisects CBD and CB DB then we can prove ACB ADB by what theorem or postulate? A D C A. SSS B. SAS C. ASA D. AAS B Revised 2015 Geometry Honors Semester 1 Review Page 4 of 16

5 34. If RUS TSU (not shown) then which is NOT true? A. RS TU B. SUR UST 38. If Q is the midpoint of MK and J L then the triangles are congruent by C. RU TS D. USR UST 35. Given R T, RSU TUS then RUS? A. SSS B. SAS C. AAS D. ASA 39. Draw in the lines of symmetry for each of the concave figures above. A. SUT B. STU C. TSU D. TUS E. The triangles are not congruent 36. A mobile maker wants to place a weight at the center of gravity of a triangular piece of metal. Which does she need? A. circumcenter B. orthocenter C. incenter D. centroid 37. If F, B and D are midpoints of EC, AC, and AE respectively, then 40. Draw the lines of symmetry for each figure. A. What point is G called? B. True or False: G the center of gravity of the triangle. C. If AG = 10 then GF = D. If DG = 18 then DC = E. If EB = 21 then GB = Revised 2015 Geometry Honors Semester 1 Review Page 5 of 16

6 41. In the diagram below RAP ISD. Which point below can be the placement of point S? 44. The picture above shows a: A. dilation B. rotation C. translation D. reflection A. (3, 8) B. (2, 8) C. (2, -5) D. (3, -5) 45. Translate the triangle (x,y) à (x + 4, y - 2). 42. The rhombus below has vertex coordinates shown. Find the coordinates of vertex S Given LMN, find the coordinates of L M N reflected over the y-axis. L M N The picture above shows a: A. dilation B. rotation C. translation D. reflection Revised 2015 Geometry Honors Semester 1 Review Page 6 of 16

7 For questions use the diagram below. NA bisects GNP N 52. Find the value of x. Round to the tenth place if needed. G A P 47. GA = 16, AP = 20, NP = 25, GN = 48. GN = 15, NP = 18, GP = 25, GA = 49. GA = 12, AP = 2x + 3, NP = 5 + x, GN = 15 What is the value of x? 5 A. B C. 8 3 D In the figures below, ΔMAP ~ Δ BOX. If m A= 75 and m X = 50, what is m B?? 50. A triangle has sides 12 ft, 14 ft and 20 ft. The smallest side of another, similar triangle measures 8 ft. What is the perimeter of the smaller triangle? 51. The diagram above may not be drawn to scale. 54. Polygon RVTUS ~ Polygon MNPQR. SU=10, and side lengths of MNPQR are shown. What is the perimeter of RVTUS? If RST ~ UPQ then find the value of x. Round to the nearest tenth. A B C D Revised 2015 Geometry Honors Semester 1 Review Page 7 of 16

8 55. Roger is 6 feet tall and stands by a flag pole. Roger casts a 5 foot shadow at the same time of day that the flag pole casts a 9 foot shadow. 57. If angle R is congruent to angle N then RO = and OF = How tall is the flag pole? A ft B. 8 ft C. 10 ft D. 7.5 ft 56. AE BF, EC DF, AE=10, EC=8, AC=9, FD=12. HC= Faith, who will play ball on a new type of field (shown below), will be the pitcher. Faith will stand an equal distance from Marie, Linda and Brenda. At which point should Faith stand in the MBL triangle? A. What conjecture states is ACE ~ BDF? B. Find BC= C. Find BH= A. circumcenter B. orthocenter C. incenter D. centroid D. Find HF= Revised 2015 Geometry Honors Semester 1 Review Page 8 of 16

9 59. Which can NOT be a triangle? 61. Find the value of x in each diagram. A. right and isosceles B. obtuse and isosceles C. equilateral and acute D. obtuse and scalene E. right and equilateral 60. Complete each statement. A. Every point in a plane which is on the is equidistant from the sides of an angle. B. Every point in a plane which is on the is equidistant from the endpoints of a segment. C. The point called the is equidistant to the sides of the triangle, D. The point called the is equidistant to the vertices of a triangle. 62. TRAP is a trapezoid with bases TR and AP. o If m R= 132 then find m A. Revised 2015 Geometry Honors Semester 1 Review Page 9 of 16

10 63. Given the following statements, name the quadrilateral that it must be. A. Parallelogram with equal sides B. Parallelogram with perpendicular diagonals. C. Parallelogram with four right angles. D. Quadrilateral with only two pair of parallel sides. 66. A quadrilateral has all sides equal. Which cannot describe that quadrilateral? A. rhombus B. square C. regular D. trapezoid E. equilateral 67. In this parallelogram, x =? 120 o (4x+12) o 64. Given that the diagram below is a parallelogram, find the value of x. (4x + 10)! 70! 68. In this parallelogram, x =? (4x+12) o 80 o (5x 15)! A. 42 B. 31 C. 9 D Rectangle RSUT has diagonals that meet at point X. If RX=4x, ST=100 and XU=5y then x= and y=? Revised 2015 Geometry Honors Semester 1 Review Page 10 of 16

11 69. Part 1. In the diagram, what are the coordinates of the midpoint of AC? 71. PROOF R. (d 1, 1.5) S.!!!,!!! T.!!!,! U. (1, 1.5)!! Part 2. What is the length of the shorter diagonal (in terms of d or w)? 70. In parallelogram BRAT, S is the intersection of the diagonals. If SB = 4x-12, SR=6x+8 and SA=3x+10, then Given: AD BC and AD BC Prove: AB CD (You may use more or less lines than eight.) Statements Reasons 72. A triangle with sides 12, 20 and 10 is A. acute B. obtuse C. right D. equilateral a. Find the value of x. b. Find the lengths of each diagonal. 73. A triangle with sides 8, 15, 16 is A. acute B. obtuse C. right D. equilateral Revised 2015 Geometry Honors Semester 1 Review Page 11 of 16

12 Which graph best represents a line parallel to the line with the equation y = 1/3x + 4? x= y= a. 6 b. 6 3 c. 2 3 d. 3 3 e. 6 f. 6 3 g. 2 3 h. 3 3 A. z= j. 6 k. 6 3 m. 2 3 n. 3 3 B. 75. Describe the triangle above. Circle all that apply. acute, obtuse, right, equilateral, scalene, isosceles, enigmatic C. D. Revised 2015 Geometry Honors Semester 1 Review Page 12 of 16

13 77. Prove the following using the flow chartproof AND two column proof. FLOW CHART TWO COLUMN PROOF Statements (You may use more or less lines than eight steps.) Reasons Revised 2015 Geometry Honors Semester 1 Review Page 13 of 16

14 78. The following conditional statements are true. Which of the conditional statements below have converses that are also true? I. If a figure is a square, then it is also a rhombus. II. If a triangle has three congruent sides, then it has three congruent angles. III. If two angles are complement, then the sum of the measures of the two angles is 90!. 82. Classify each transformation. (The shaded figure is the pre-mage) 79. What is true about the conditional statement below? If an object is a pentagon, then the object is a polygon. A. The converse is always true. B. The converse is sometimes true. C. The converse is never true. D. It cannot be determined if the converse is true. 80. Produce a counterexample to show that the following statement is not true. If a number is divisible by 2, than it is divisible by In the graph below, the graph of y = x + 2 is shown. If this graph is reflected across the x-axis, what is the y- coordinate of the point on the reflected graph at x = 3? y x Revised 2015 Geometry Honors Semester 1 Review Page 14 of 16

15 83. Classify the transformation. (The shaded figure is the pre-mage) 85. Draw a 180 o counterclockwise rotation of the figure below and identify the new coordinates of each vertex. 84. In the figure below, the dashed figure is the preimage, and the solid outlined figure is the image. What is the transformation rule of the translation below? 86. Based on the measurements below, does MT bisect AMH? Why or why not? 87. Determine the value of x. Revised 2015 Geometry Honors Semester 1 Review Page 15 of 16

16 88. Determine the values of x and y. 91. In the figure below, ABCD ~ JKLM. What is the perimeter of JKLM? 89. What is the value of x in the figure below? 92. In the figure below, ΔA B C is a dilation of ΔABC. What is the scale factor of the dilation? 90. In the figure below, what is the length of PR? Revised 2015 Geometry Honors Semester 1 Review Page 16 of 16

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