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Geometry Performance Expectations by reporting Strand Reporting Strands Logical arguments and proof Proving and applying properties of 2-dimensional figures Figures in a coordinate plane and measurement Course-Specific content Performance Expectations G.1.D G.1.E G.1.F G.3.A G.3.B G.3.C G.3.D G.3.E G.3.F G.3.G G.4.B G.4.C G.6.E G.6.F G.1.A G.2.A G.2.B G.2.C G.2.D G.3.B G.3.H G.3.I G.3.J G.3.K G.4.A G.4.D G.5.A G.5.B G.5.C G.5.D G.6.A G.6.C G.6.D Anticipated number of questions 6-8 21-24 7-9 6* Question 1. Determine the value of x if ฮABC is equilateral. PE G.3.A Answer G.1.D C: If you are a pet owner, then you have a dog. False, you could have a hamster. G.2.B D: m ๏ 4 + m ๏ 6 = 180 ๐ฅ=2 B 6x + 3 7.5x A C 10x โ 5 Write your answer on the line. 2. Write the converse of the conditional statement. Determine if the converse is true or false. If it is false, find a counterexample. โIf you have a dog, then you are a pet owner.โ 3. Given aโb, determine which equation must be true. a 3 b 7 1 2 4 5 6 8 4. Determine measure of angle 2. Write your answer on the line. G.3.A m ๏ 2=50ห 70° 2 1 60° 3 4 40° 5. ฮDEF has vertices D(4, 1), E(2, โ1), and F(โ2, โ1). Classify ฮDEF based on its sides. G.4.C C: scalene 1 Determine the equation of a line through the point (3, โ4) that is perpendicular to the line y = 3x + 7. G.4.A C: ๐ฆ = โ 3 ๐ฅ โ 3 Joe and Sara were standing on a pier sailing a toy sail boat. The boat was 6 feet from the base of the pier and the pier was 4 feet above the water. O 6 ft G.3.A โ 33.7ห G.1.E B: In the figure Joanna drew, the 6. 7. A 4 ft B T Determine the angle of depression from the pier to the toy sail boat. Show your work using words, numbers and/or diagrams. 8. Joannaโs teacher said โThe diagonals of a square bisect each other.โ Joanna drew this figure and said โThe diagonals of this figure bisect each other, so it must be a square.โ Joanna made an error in her mathematical argument. What is the error? diagonals do not bisect each other. 9. Determine the midpoint of G.4.B JK , where J(โ1, 2) and K(6, 8). 10. Look at the diagram. K B: ( 2 1 , 5) 2 G.3.B C: Angle-Side-Angle Congruence G.4.B Q (1, -2) G.1.A B: This is an example of inductive M L J N What theorem or postulate can you use to prove โ๐พ๐ฟ๐ โ โ๐๐ฟ๐ฝ? 11. Three vertices of a square have coordinates (3, 1), (4, -4) and (-1, -5). The diagonals of the square intersect at point Q. Determine the coordinates of point Q. 12. 3, 5, 7, and 11 are prime numbers. 4, 6, 8, 9, and 10 are composite numbers. Tiana makes the conjecture that prime numbers must be odd. Which statement is true? 13. One leg of a 45° โ 45° โ 90° triangle is 8 cm long. Determine the length of the hypotenuse. reasoning and the conjecture is not valid. G.3.C B: 8โ2 G.1.D 14. Look at the conditional statement. C: If an angle is acute, then it measures 30°. โIf an angle measures 30°, then it is acuteโ Which statement is the converse? 15. Which equation represents the line through the points (-1, -2) and (2, 7)? G.4.A A: y = 3x + 1 16. Which statement is true about all parallelograms? G.3.F C: The diagonals bisect each other. 17. Quadrilateral ABCD is a rhombus and mโ BCE = 50°. G.3.G mโ EBC=40ห G.1.D D: If a figure is not a pentagon, then A B E D C Determine the mโ EBC. 18. Look at the conditional statement. it does not have five sides. โIf a figure is a pentagon, then it has five sidesโ Which statement is the inverse? 19. Triangle JKE is an obtuse isosceles triangle with mโ E = 10° and ฬ ฬ ฬ ฬ ๐พ๐ธ > ฬ ฬ ฬ ๐ฝ๐พ . G.3.A B: 160° G.3.B Statement 5: mโ ABD= mโ CBE What is the mโ J? 20. A proof is shown. Fill in the blanks for steps 5 and 6 to complete the proof. Given: ฬ ฬ ฬ ฬ . B is the midpoint of ๐ด๐ธ B is the midpoint of ฬ ฬ ฬ ฬ ๐ถ๐ท . Prove: โ๐ด๐ต๐ท โ โ๐ธ๐ต๐ถ. Reason 6: SAS congruency 1 21. Which ordered pair is the midpoint of the line segment with endpoints (2,-5) and (-6, 4)? G.4.B C: (โ2, โ 2) 22. The diagonal of a square is 7 cm. G.3.C D: 7โ2 2 7 cm Determine the length of one side of the square. 23. Which statement is true? G.1.F A: A postulate is accepted as true 24. Two unique planes intersect. Which geometric term describes the intersection? G.2.D without proof. A: line 25. Look at the diagram. G.3.F C: a = 13.5, b = 106 (6๐ โ 7)° ๐° (4๐ + 20)° Determine the values for a and b that would make the quadrilateral a parallelogram. 26. Look at the triangle. 18 13 5 y G.3.D ๐ฆ = 6โ5 Determine the length of y. Express your answer in simplified radical form. 27. Lines l, m, and n lie in the same plane. Line m is perpendicular to line l. Line n is perpendicular to line l. Which statement is true? 28. G.2.A B: Line m and line n are parallel. While walking around G.3.E Seattle, Mary climbed several steep streets. One of the steepest streets, Roy Street, has a slope angle of 11.9° according to the tour guide. After walking 100 feet up the hill, she wanted to determine how high she had climbed. 11.9° 100 feet sin 11.9ห = ๐ป๐๐๐โ๐ก ๐ถ๐๐๐๐๐๐ โ 20.6 ๐๐ก Rounded to nearest foot: 21 ft Height climbed Horizontal distance Use a trigonometric ratio (sine, cosine, tangent) to determine how high Mary climbed. Be sure to write the equation and show the steps you used to solve the equation. Round your answer to the nearest foot. 29. Determine how many miles a person will run G.6.F ๐ป๐๐๐โ๐ก ๐ถ๐๐๐๐๐๐ 100 โ3.1 miles during a 5-kilometer race. Write your answer on the line. 1 km โ 0.62 mi 30. Which statement is an example of inductive reasoning? G.1.A B: Squares have equal sides. This 31. The rhombus QRST is made of two congruent triangles. Given m ๏ QRS = 34° determine the measure of ๏ S. Q G.3.F/G.3.G figure has equal sides, therefore this figure is a square. C: 146° R S T 32. Determine whether the conjecture is true or false. Give a counterexample for a false conjecture. G.1.E False. Any three points define a plane. Points A, B, and C define a unique plane. Point D does not have to be on this plane. Given: points A, B, C, and D Conjecture: A, B, C, and D are coplanar 33. Identify the congruent triangles in the diagram and write a congruence statement. G.3.B B: ฮ LSK ๏ ฮ MSN G.3.E D: M L S K N 34. Determine cos I in ฮGHI. G 72 75 75 21 I H 72 35. Write the contrapositive of the conditional statement. G.1.D C: Non-supplementary angles and not two angles measuring 180 degrees. True Determine if the contrapositive is true or false. If it is false, find a counterexample. โTwo angles measuring 180 degrees are supplementaryโ 36. Complete this chart. G.3.J 37. Determine which statement is a property of all rectangles. G.3.G Triangular Prism: Edges:9, faces:5, vertices: 6 Square Pyramid: Edges: 8, faces:5, vertices: 5 Cube: Edges:12, faces:6, vertices:8 Hexagonal Pyramid: Edges:12, faces:7, vertices:7 Hexagonal Prism: Edges:18, faces:8, vertices:12 D: Four right angles. 38. The figure is a rectangular prism with dimensions 12 inches long, 5 inches wide and 7 inches tall. Determine the length of G.3.D BI=โ218 BI . BIโ14.76 inches B C A D 7 G F 5 H I 12 Write your answer on the line. 39. Given B(โ4, โ6), determine which reflection would result in Bโ(6, 4). G.5.A 40. Determine the exact length of x in ฮHJK. G.3.C C: Reflected over the line y = โx. C: 10 K 60° x J 5 30° H 1 ๐๐โ ๐๐ 73. 3ฬ ๐๐โ 3 41. If you are going 50 miles per hour, determine how many feet per second you are traveling. 42. The ratio of a pair of corresponding sides in two similar triangles is 5:3. The area of the smaller triangle is 108 in2. What is the area of the larger triangle? G.6.F G.6.D ๐๐๐๐๐๐ ๐ก๐๐๐๐๐๐๐: 300๐๐2 43. Jessie is working on the roof of her house. She has measured the angle of the roof and the length of the roof. Determine the width of the house, w. G.3.E ๐ค โ 24.6 ๐๐๐๐ก 15 ft. 73 15 ft. 35° w ๏ท ๏ท 44. The segment bisector is the midpoint. G.1.D 45. ฮRST has vertices R(3, 3), S(6, โ2), and T(0, โ2). Classify ฮRST based on its sides. G.4.C 46. Look at the given information for quadrilateral ABCD. ฬ ฬ ฬ ฬ ฬ ฬ ฬ ฬ ๐ด๐ต ||๐ถ๐ท ฬ ฬ ฬ ฬ ๐ด๐ถ โ ฬ ฬ ฬ ฬ ๐ต๐ท ฬ ฬ ฬ ฬ ๐ด๐ท is not parallel to ฬ ฬ ฬ ฬ ๐ต๐ถ G.7.E/G.3.G Draw and label a shape that satisfies all of the given information. Determine the most specific name for the shape. 47. Martina has a calculator box that has a volume of 29 Inverse: The non-segment bisector is not the midpoint True A: isosceles A C » B » Isosceles Trapezoid G.6.F โ 475.22๐๐3 D cubic inches. 1 inch = 2.54 centimeters Determine the volume of the calculator box to the nearest cubic centimeter. 48. Determine the image of Y(โ4, 7) under the translation of : (x, y) ๏ฎ (x + 3, y โ 5). G.5.B A: Y๏ข(โ1, 2) 49. Look at the figure. G.3.B A: FH = 12 What additional information do you need to show the triangles below are similar using the Side-AngleSide Similarity Theorem? E G 18 8 F 10 D 12 H 50. Find sin C as a decimal rounded to the nearest hundredth. C 8.3 A G.3.E D: 0.87 16.9 B 14.7 51. Two similar figures have a ratio of volumes of 64:27. What is the ratio of similarity? 1 52. Michael is 5 feet tall. 2 Michael measures his G.6.D G.3.B Ratio of Similarity is 4:3 โ 17.2 ๐ฆ๐๐๐๐ shadow as 8 feet long. A tree in his backyard has a shadow that is 25 yards long. How tall is the tree? 5 ½ ft 8 ft G.1.E 53. Look at the pair of triangles. to determine similarity or congruence. B A D: There is not enough information D C Which statement is true? 54. Steven built a box for his vegetable garden in the shape of a rectangular prism. The volume of the vegetable garden was 24 cubic feet. He built another garden box that was two times longer and two times higher. He thinks the volume will be twice as much. Explain why Steven is not correct. G.6.D Original box volume: xyz New box volume: (2x)(2y)(z)= 4xyz If Steven wanted to double the volume of his garden, he would need to double only one of the dimensions (probably the length or width) If Steven wants his second garden box to have twice the volume, what should he do instead? 55. To the nearest degree, what is mโ G? Steven is not correct. By doubling two dimensions, he has created a rectangular prism with 4 times the volume. G.3.E B: 57° G.4.B D: L (8, 3) E 12. 1 F 7.8 G 56. JKLM is an isosceles trapezoid with J(0, โ1), K(โ 2, 3) and M(6, โ1). Determine the coordinates of L. 57. Given aโb, determine which relationship must be true. a 3 b 7 G.2.B B: ๏ 2 and ๏ 8 are supplementary. G.3.B C: 1 2 4 5 6 8 58. Determine which triangle is similar to ฮDEF. 36 D 13 39 5 F E 12 59. Name all segments skew to G.1.F C B BC . A 15 D: GF , HI , DI , AF D H G I F 60. Determine which theorem or postulate can be used to prove that these two triangles are similar. G.3.B A: AA 8 63° 4 27° 6 61. Cody is standing 14 feet from the base of the tree. The top of the tree makes a G.3.C ๐๐๐๐ โ๐๐๐โ๐ก = 14โ3๐๐๐๐ก ๐๐๐๐ โ๐๐๐โ๐ก โ 24.25 ๐๐๐๐ก 60° angle with the ground at the point where he is standing. 60° 14 ft Determine the height of the tree. Round your answer to two decimal places. G.2.B 62. Given aโb m ๏ 3 = 5x + 10 and m ๏ 5 = 3x + 10, determine the value of x. 1 2 3 4 a b 7 63. In circle C, m AB = 72. Determine m ๏ BCD. C: 20 5 6 8 m ๏ BCD=108ห G.3.H A C Write your answer on the line. D B 64. Determine which set of measures could represent the sides of a right triangle. 65. Determine the exact value of x in ฮLMN. N x G.3.D D: 9, 12, 15 G.3.C C: 25 3 50 60° L 66. ฮRST has vertices R(3, 3), S(6, โ2), and T(0, โ2). Classify ฮRST based on its G.4.C M A: isosceles sides. 67. In the diagram: G.3.B Statement ฬ ฬ ฬ ฬ ๐ด๐ต โ ฬ ฬ ฬ ฬ ๐ธ๐ต Given: AB ๏ EB A Prove: ๏D ๏ ๏C ๏ABD ๏ ๏CBE ๏D ๏ ๏C ๏ABD ๏ ๏EBC C B โDBAโ โCBE Justification Given Given Vertical angles are congruent AAS congruency D E 68. Determine the value of y. G.3.H D: 4.5 G.3.G C: 90° 3 6 y 9 69. For rhombus GHJK, determine m ๏ 1. G H 1 K J 70. Given quadrilateral XYWZ, determine whether 8 ๐๐๐๐๐ ๐๐ ๐ค๐ฅ ฬ ฬ ฬ ฬ = โ 1 3 ๐๐๐๐๐ ๐๐ ฬ ฬ ฬ ๐ฆ๐ง = 3 G.4.C WX and YZ are parallel, perpendicular or neither. Neither W(0, โ3), X(โ1, 5), Y( 2, 5) Z(โ1, 2) 71. Determine the value of x and y so that QRST will be a parallelogram. G.3.F/G.3.G A: x = 6, y = 42 Q R 24° (y-10)° 32° 4x° T S 72. Two angles measuring 90° are complementary. G.1.D 73. Which statement is an example of deductive reasoning? G.1.A 74. G.3.B If Inverse: Two angles whose sum is not 90ห are not complementary True B: Dogs are mammals. Mammals breathe oxygen. Therefore dogs breathe oxygen. B AF ๏ DE , AB ๏ FC and C: SAS C AB โ FC , determine which theorem or postulate can be used to prove ๏ABE ๏ ๏FCD . A 75. Identify which of the following is a property of a parallelogram. G.3.F F E D D: The diagonals bisect each other.