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GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 Instructional Materials for WCSD Math Common Finals The Instructional Materials are for student and teacher use and are aligned to the 2016-2017 Course Guides for the following courses: ο· Geometry S1 (#2211) ο· Foundations in Geometry S1 (#7771) When used as test practice, success on the Instructional Materials does not guarantee success on the district math common final. Students can use these Instructional Materials to become familiar with the format and language used on the district common finals. Familiarity with standards and vocabulary as well as interaction with the types of problems included in the Instructional Materials can result in less anxiety on the part of the students. The length of the actual final exam may differ in length from the Instructional Materials. Teachers can use the Instructional Materials in conjunction with the course guides to ensure that instruction and content is aligned with what will be assessed. The Instructional Materials are not representative of the depth or full range of learning that should occur in the classroom. *Students will be allowed to use a non-programmable scientific calculator on Geometry Semester 1 and Geometry Semester 2 final exams. Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS 2016-2017 Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) Geometry Reference Sheet Note: You may use these formulas throughout this entire test. Linear Quadratic π¦2 β π¦1 π₯2 β π₯1 Vertex-Form π¦ = π(π₯ β h)2 + π π₯1 + π₯2 π¦1 + π¦2 π=( , ) 2 2 Standard Form π¦ = ππ₯ 2 + ππ₯ + π π = β(π₯2 β π₯1 )2 + (π¦2 β π¦1 )2 Intercept Form π¦ = π(π₯ β π)(π₯ β π) Slope π= Midpoint Distance Slope-Intercept Form π¦ = ππ₯ + π Exponential (h, k) Form Probability π¦ = ππ π₯βh + π π(π΄ πππ π΅) = π(π΄) β π(π΅) π(π΄ πππ π΅) = π(π΄) β π(π΅|π΄) π(π΄ ππ π΅) = π(π΄) + π(π΅) β π(π΄ πππ π΅) Volume and Surface Area π = ππ 2 β 4 π = ππ 3 3 ππ΄ = 2(ππ 2 ) + β(2ππ) ππ΄ = 4ππ 2 1 1 π = ππ 2 β 3 1 ππ΄ = ππ 2 + (2ππ β π) 2 Released 8/22/16 π = π΅β 3 1 ππ΄ = π΅ + (ππ) 2 Where π΅ =base area and π =base perimeter GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 Multiple Choice: Identify the choice that best completes the statement or answers the question. Figures are not necessarily drawn to scale. 1. Describe the transformation π: (β2, 5) β (2, β5). A. A reflection across the y-axis B. A reflection across the x-axis C. A rotation 180° with center of rotation (0, 0) D. A rotation 90° with center of rotation (0, 0) 2. Find the coordinates of the image of the point (β5, 7) when it is reflected across the line π¦ = 11. A. (β5, 18) C. (β5, β4) B. (β5, 15) D. (β5, β7) 3. What are coordinates for the image of quadrilateral ABCD after the translation of (π₯, π¦) β (π₯ + 7, π¦ β 2) ? A. π΄β² (8, β5), π΅ β² (2, β1), πΆ β² (12, β4), π·β² (10, β7) B. π΄β² (β6, β1), π΅ β² (β5, 1), πΆ β² (β2, 0), π·β² (β4, β3) C. π΄β² (β6, β5), π΅ β² (2, β1), πΆ β² (12, β4), π·β² (10, β7) D. π΄β² (8, β5), π΅ β² (9, β3), πΆ β² (12, β4), π·β² (10, β7) Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 4. 2016-2017 Figure ABC is rotated 90° clockwise about the point (2, 0). What are the coordinates of π΄β² after the rotation? A. π΄β²(β1, 4) B. π΄β²(3, β6) C. π΄β²(5, β4) D. π΄β²(6, β3) 5. What are the coordinates for the image of βπΊπ»πΎ after a rotation 90° counterclockwise about the origin and a translation of (π₯, π¦) β (π₯ + 3, π¦ + 2) ? A. πΎ β²β² (β2, 0), π» β²β² (2, β1), πΊ β²β² (0, β4) B. πΎ β²β² (2, 0), π» β²β² (β2, 1), πΊ β²β² (0, 4) C. πΎ β²β² (β4, β4), π» β²β² (β8, β3), πΊ β²β² (β6, 0) D. πΎ β²β² (4, 4), π» β²β² (8, 3), πΊ β²β² (6, 0) 6. The point π(β2, β5) is rotated 90° counterclockwise about the origin, and then the image is reflected across the line π₯ = 3. What are the coordinates of the final image πβ²β²? A. (1, β2) C. (β2, 1) B. (11, β2) D. (2, 11) Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 7. Draw line β‘πΉπΊ and point π» not on the line. Reflect point H across the line β‘πΉπΊ to form point π»β². Based on your diagram, which of the following is true? Μ Μ Μ Μ Μ Μ Μ Μ β πΉπΊ A. π»πΉ B. Μ Μ Μ Μ π»πΉ β Μ Μ Μ Μ Μ π»β²πΊ Μ Μ Μ Μ β Μ Μ Μ Μ Μ C. πΉπΊ π»β²πΊ D. Μ Μ Μ Μ π»πΊ β Μ Μ Μ Μ Μ π»β²πΊ 8. Which composition of transformations maps βπ·πΈπΉ into the first quadrant? A. Reflection across the line π¦ = π₯ and then a translation of (π₯ + 2, π¦ + 5). B. Translation of (π₯ β 1, π¦ β 6) and then a reflection in the line π¦ = π₯. C. Clockwise rotation about the origin by 180° and then reflection across the y-axis. D. Counterclockwise rotation about the origin by 90° and then a translation of (π₯ β 1, π¦ + 6). Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 9. Which of the following options correctly explains how to find the value of π₯ in the figure below? A. Since πΈπ΄ and πΈπ· are opposite rays, and πΈπ΅ and πΈπΆ are opposite rays, β π΄πΈπ΅ and β π·πΈπ΅ are vertical angles. Vertical angles are congruent and have the same measure, so πβ π΄πΈπ΅ = πβ π·πΈπΆ. Using substitution gives the equation, 2π₯ = 30. Dividing by 2 on both sides gives π₯ = 15. B. Since πΈπ΄ and πΈπ· are opposite rays, and πΈπ΅ and πΈπΆ are opposite rays, β π΄πΈπ΅ and β π·πΈπ΅ are vertical angles. Vertical angles are complimentary meaning their measures add up to 90°, so πβ π΄πΈπ΅ + πβ π·πΈπΆ = 90°. Using substitution gives the equation, 2π₯ + 30 = 90. Subtracting both sides by 30, and then dividing both sides by 2 gives π₯ = 30. C. Since β π΄πΈπ· is a straight angle, its measure is 180°. By the Angle Addition Postulate, πβ π΄πΈπ΅ + πβ π΅πΈπΆ + πβ πΆπΈπ· = πβ π΄πΈπ·. Using substitution gives the equation, 2π₯ + 4π₯ + 30 = 180. After combining like terms the equation becomes 6π₯ + 30 = 180. Subtracting both sides by 30, and then dividing both sides by 6 gives π₯ = 25. D. Since β π΄πΈπ· is a straight angle, its measure is 90°. By the Angle Addition Postulate, πβ π΄πΈπ΅ + πβ π΅πΈπΆ + πβ πΆπΈπ· = πβ π΄πΈπ·. Using substitution gives the equation, 2π₯ + 4π₯ + 30 = 90. After combining like terms the equation becomes 6π₯ + 30 = 90. Subtracting both sides by 30, and then dividing both sides by 6 gives π₯ = 10. 10. In the figure πβ πΉπΊπΌ = (2π₯ + 9)° and πβ π»πΊπΌ = (4π₯ β 15)°. Find πβ πΉπΊπΌ and πβ π»πΊπΌ. A. πβ πΉπΊπΌ = 71° and πβ π»πΊπΌ = 109° B. πβ πΉπΊπΌ = 45° and πβ π»πΊπΌ = 45° C. πβ πΉπΊπΌ = 33° and πβ π»πΊπΌ = 33° D. πβ πΉπΊπΌ = 41° and πβ π»πΊπΌ = 49° Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 11. πΈπ΅ is the angle bisector of β π΄πΈπΆ. What is the value of x? A. π₯ = 35 B. π₯ = 51.5 C. π₯ = 70.5 D. π₯ = 142 12. Based on the figure below, which statements are true if π β₯ π and π β₯ π ? I. πβ 1 = πβ 5 II. πβ 2 + πβ 3 = 180° III. πβ 4 = πβ 8 IV. πβ 6 + πβ 9 = 180° V. πβ 1 + πβ 9 = 180° A. All of the above C. II, III, and IV B. I, III, and IV D. III, IV, and V 13. In the figure, πβ π΄π΅πΆ = πβ π΄πΆπ΅ = π₯. Find the πβ πΈπ΄π΅ in terms of x. A. 180 β 2π₯ B. 2π₯ C. π₯ D. π₯ + 90 Released 8/22/16 2016-2017 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 For #14-15 use the following: Given: πΎπ bisects β π½πΎπΏ Prove: πβ 2 = πβ 3 Statements Reasons πΎπ bisects β π½πΎπΏ β 1 β β 2 Given πβ 1 = πβ 2 Definition of Congruence β 1 β β 3 15. πβ 1 = πβ 3 Definition of Congruence πβ 2 = πβ 3 Substitution Property of Equality 14. 14. Choose one of the following to complete the proof. A. Definition of angle bisector- If a ray is an angle bisector, then it divides an angle into two congruent angles. B. Definition of opposite rays- If a point on the line determines two rays are collinear, then the rays are opposite rays. C. Definition of ray- If a line begins at an endpoint and extends infinitely, then it is ray. D. Definition of segment bisector- If any segment, line, or plane intersects a segment at its midpoint then it is the segment bisector. 15. Choose one of the following to complete the proof. A. Definition of complementary angles- If the angle measures add up to 90°, then angles are supplementary B. Supplemental Angle Theorem- If two angles are supplementary to a third angle then the two angles are congruent C. Definition of supplementary angles- If the angles are supplementary, then the angleβs measures add to 180°. D. Vertical Angle Theorem- If two angles are vertical angles, then they have congruent angle measures. Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) For #16 use the following: Given: β 1 and β 2 are supplementary, and πβ 1 = 135° Prove: πβ 2 = 45° 16. Statements Reasons β 1 and β 2 are supplementary Given [1] Given πβ 1 + πβ 2 = 180° [2] 135° + πβ 2 = 180° Substitution Property of Equality πβ 2 = 45° [3] Fill in the blanks to complete the two column proof: A. [1] πβ 2 = 135° [2] Definition of Supplementary Angles [3] Subtraction Property of Equality B. [1] πβ 1 = 135° [2] Definition of Supplementary Angles [3] Substitution Property of Equality C. [1] πβ 1 = 135° [2] Definition of Supplementary Angles [3] Subtraction Property of Equality D. [1] πβ 1 = 135° [2] Definition of Complementary Angles [3] Subtraction Property of Equality 17. Find πΆπΈ given the following information: Μ Μ Μ Μ is the perpendicular bisector of π·π΅ Μ Μ Μ Μ ο· π΄πΆ ο· πΈπ΄ = 16 ο· π·πΆ = 13 ο· π΄π΅ = 20 A. πΆπΈ = 15.9 B. πΆπΈ = 5 C. πΆπΈ = 17.7 D. πΆπΈ = 16 Released 8/22/16 2016-2017 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 β‘ . 18. Point A is reflected over the line π΅πΆ β‘ ? Which of the following is not true of line π΅πΆ β‘ is perpendicular to line β‘π΄π΄β² A. line π΅πΆ β‘ is perpendicular to line π΄π΅ β‘ B. line π΅πΆ β‘ bisects line segment Μ Μ Μ Μ C. line π΅πΆ π΄π΅ β‘ bisects line segment Μ Μ Μ Μ Μ D. line π΅πΆ π΄π΄β² 19. Which statement is true based on the figure? A. π β₯ π B. π β₯ π C. π β₯ π D. π β₯ π 20. Draw two lines and a transversal such that β 1 and β 2 are alternate interior angles, β 2 and β 3 are corresponding angles, and β 3 and β 4 are alternate exterior angles. What type of angle pair is β 1 and β 4? A. β 1 and β 4 are supplementary angles B. β 1 and β 4 are vertical angles Released 8/22/16 C. β 1 and β 4 are corresponding angles D. β 1 and β 4 are alternate exterior angles GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 For #21-22 use the following: Given: π β₯ π Prove: πβ 3 + πβ 6 = 180 Statements Reasons πβ₯π Given 21. If two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent. πβ 3 = πβ 5 Definition of Congruence β 5 and β 6 are supplementary If two angles form a linear pair, then they are supplementary. πβ 5 + πβ 6 = 180 22. πβ 3 + πβ 6 = 180 Substitution Property of Equality 21. Choose one of the following to complete the proof. A. β 4 β β 5 B. β 2 β β 8 C. β 3 β β 6 D. β 3 β β 5 22. Choose one of the following to complete the proof. A. Vertical Angle Theorem- If two angles are vertical angles, then they have congruent angle measures B. Supplemental Angle Theorem- If two angles are supplementary to a third angle then they are congruent C. Definition of supplementary angles- If two angles are supplementary, then their angle measures add to 180°. D. Definition of complementary angles- If two angles are a complementary, then their angle measures add to 90° Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 23. Solve for x and y so that π β₯ π β₯ π. A. π₯ = 9, π¦ = 10.1 C. π₯ = 29, π¦ = 3.2 B. π₯ = 9, π¦ = 9.9 D. π₯ = 29, π¦ = 11.0 24. In the diagram below, line π is parallel to line π and line π‘ is perpendicular to π΄π΅ . What is the measure of β π΅π΄πΆ? A. πβ π΅π΄πΆ = 37° C. πβ π΅π΄πΆ = 45° B. πβ π΅π΄πΆ = 53° D. πβ π΅π΄πΆ = 127° 25. What are the coordinates of the point P that lies along the directed segment from πΆ(β3, β2) to π·(6, 1) and partitions the segment in the ratio of 2 to 1? A. (0, 3) C. (1.5, 0.5) B. (3, 0) D. (4.5, 1.5) Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 26. An 80 mile trip is represented on a gridded map by a directed line segment from point π(3, 2) to point π(9, 13). What point represents 60 miles into the trip? A. (8, 14.6) C. (9, 11.25) B. (3.75, 9.75) D. (7.5, 10.25) 27. Given the two lines below, which statement is true? πΏπππ 1: π₯ β 3π¦ = β15 and πΏπππ 2: π¦ = 3(π₯ + 2) β 1 A. The lines are parallel. B. They are the same line. C. The lines are perpendicular. D. The lines intersect but are not perpendicular. 28. Which equation of the line passes through (5, β8) and is parallel to the graph of the line 2 π¦ = 3 π₯ β 4? A. π¦ = 2 34 π₯β 3 3 3 1 B. π¦ = β π₯ β 2 2 Released 8/22/16 C. π¦ = 2 π₯β8 3 3 D. π¦ = β π₯ β 8 2 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 29. Which equation of the line passes through (4, 7) and is perpendicular to the graph of the line that passes through the points (1, 3) and (β2, 9) ? A. π¦ = 2π₯ β 1 B. π¦ = 1 π₯+5 2 C. π¦ = 1 π₯β5 2 D. π¦ = β2π₯ + 15 30. Which of the following is true? A. All triangles are congruent. B. All congruent figures have three sides. C. If two figures are congruent, there must be some sequence of rigid motions that maps one to the other. D. If two triangles are congruent, then they must be right triangles. 31. If βπΆπΈπ· β βππ π, which of the following is true? A. β πΆ β β π, β πΈ β β π , β π· β β π B. β πΆ β β π, β πΈ β β π, β π· β β π C. β πΆ β β π, β πΈ β β π , β π· β β π D. β πΆ β β π , β πΈ β β π, β π· β β π Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 Μ Μ Μ Μ . What information is needed to prove that 32. In the figure β πΊπ΄πΈ β β πΏππ· and Μ Μ Μ Μ π΄πΈ β π·π βπ΄πΊπΈ β βππΏπ· by SAS? Μ Μ Μ Μ β πΏπ· Μ Μ Μ Μ A. πΊπΈ B. Μ Μ Μ Μ π΄πΊ β Μ Μ Μ Μ ππΏ C. β π΄πΊπΈ β β ππΏπ· D. β π΄πΈπΊ β β ππ·πΏ 33. Which conclusion can be drawn from the given facts in the diagram? Μ Μ Μ Μ bisects β πππ A. ππ B. β πππ β β π ππ Μ Μ Μ Μ Μ Μ Μ Μ β π π C. ππ D. ππ = ππ 34. In the figure β π» β β πΏ and π»π½ = π½πΏ. Which of the following statements is about congruence is true? A. βπ»πΌπ½ β βπΏπΎπ½ by ASA B. βπ»πΌπ½ β βπΎπΏπ½ by SSS C. βπ»πΌπ½ β βπΎπΏπ½ by SAS D. βπ»πΌπ½ β βπΏπΎπ½ by SAS Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 35. Refer To the figure to complete the congruence statement, βπ΄π΅πΆ β _________. A. βπ΄πΆπΈ B. βπΈπ·πΆ C. βπΈπ΄π· D. βπΈπ·π΄ 36. Which theorem can be used to conclude that βπΆπ΄π΅ β βπΆπΈπ·? A. SAA B. SAS C. SSS D. AAA 37. In the figure, identify which congruence statement is true. Then find πβ πππ. A. βπππ β βπππ by HL πβ πππ = 22° B. βπππ β βπππ by HL πβ πππ = 78° C. βπππ β βπππ by HL πβ πππ = 22° D. βπππ β βπππ by HL πβ πππ = 68° Released 8/22/16 2016-2017 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 38. Determine which postulate or theorem can be used to prove the pair of triangles congruent. A. AAS B. SAS C. ASA D. SSS 39. Which of the following sets of triangles can be proved congruent using the AAS Theorem? A. C. B. D. 40. Given βπππ, Anna is proving πβ 1 + πβ 2 = πβ 4. Which statement should be part of her proof? A. πβ 1 = πβ 2 B. πβ 1 = πβ 3 C. πβ 1 + πβ 3 = 180° D. πβ 3 + πβ 4 = 180° Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 For #41-42 use the following: Given: π is the midpoint of Μ Μ Μ Μ Μ ππ; β πππ β β πππ Prove: βπππ β βπππ Statements Reasons Μ Μ Μ Μ Μ ; β πππ β β πππ π is the midpoint of ππ Given 41. Definition of Midpoint β πππ β β πππ Μ Μ Μ Μ β ππ Μ Μ Μ Μ ππ Given βπππ β βπππ 42. Reflexive property of congruence 41. Choose one of the following to complete the proof. Μ Μ Μ Μ Μ Μ Μ Μ Μ β ππ A. ππ B. Μ Μ Μ Μ Μ ππ β Μ Μ Μ Μ ππ C. Μ Μ Μ Μ Μ ππ β Μ Μ Μ Μ ππ Μ Μ Μ Μ β ππ Μ Μ Μ Μ D. ππ 42. Choose one of the following to complete the proof. A. Reflexive property of equality B. SSA Congruence C. SAS Congruence D. AAS Congruence Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 43. In the figure, βπππ β βπππ. What is the value of y? A. π¦ = 8 B. π¦ = 10 C. π¦ = 42 D. π¦ = 52 44. If a triangle has two sides with lengths of 8 ππ and 14 ππ. Which length below could not represent the length of the third side? A. 7 ππ C. 15 ππ B. 13 ππ 45. Find the range of values containing x. A. 2 < π₯ < 5 B. π₯ < 5 C. 0 < π₯ < 9 D. π₯ > 0 Released 8/22/16 D. 22 ππ GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 46. Reflecting over which line will map the rhombus onto itself? A. π¦ = β2π₯ B. π¦ = 0 1 C. π¦ = π₯ 4 D. π¦ = π₯ 47. What is the measure of π»π½ in Parallelogram πΉπΊπ»π½, given the following: πΉπΊ = π₯ + 7 πΊπ» = 5π₯ + 3 πβ πΉ = 46° πβ π» = (3π₯ + 10)° A. π»π½ = 63 B. π»π½ = 19 C. π»π½ = 12 D. π»π½ = 8 48. What is the value of x in the rectangle? A. π₯ = 42 B. π₯ = 24 C. π₯ = 8 D. π₯ = 4 Released 8/22/16 2016-2017 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 49. Which of the following is not always true of Parallelogram π΄π΅πΆπ·? Μ Μ Μ Μ , Μ Μ Μ Μ Μ Μ Μ Μ A. Μ Μ Μ Μ π΄π΅ β π΅πΆ π·πΆ β π΅πΆ Μ Μ Μ Μ β Μ Μ Μ Μ B. Μ Μ Μ Μ π΄π΅ β Μ Μ Μ Μ π·πΆ , π΅πΆ π΄π· C. πβ π΄ + πβ π΅ = 180° D. π΄π΅ + π΅πΆ = π΄π· + π·πΆ 50. π½πΎπΏπ is a rhombus. If πβ π½ππΏ = 70 and πβ π½πΎπ = (5π₯ + 16)°, find the value of π₯. A. π₯ = 18.8 B. π₯ = 10.8 C. π₯ = 7.8 D. π₯ = 3.8 51. Based on the figure below, which statements are true? I. The figure is a rectangle II. The figure is a parallelogram III. 6π₯ β 4 = 9π₯ + 3 IV. 9π₯ + 3 = 10π₯ β 2 V. π₯=8 VI. The longest side has a length of 60. A. I, III, and V C. II, IV, and VI B. I, IV, and VI D. II, III, and V Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 52. A wooden frame has screws at A, B, C, and D so that the sides of it can be pressed to change the angles occurring at each vertex. Μ Μ Μ Μ π΄π΅ β Μ Μ Μ Μ πΆπ· and Μ Μ Μ Μ π΄π΅ β₯ Μ Μ Μ Μ πΆπ·, even when the angles change. Why is the frame always a parallelogram? A. The angles always stay the same, so π΄π΅πΆπ· is a parallelogram. B. All sides are congruent, so π΄π΅πΆπ· is a parallelogram. C. One pair of opposite sides is congruent and parallel, so π΄π΅πΆπ· is a parallelogram. D. One pair of opposite sides is congruent, so π΄π΅πΆπ· is a parallelogram. 53. Which statement is true? A. All quadrilaterals are rectangles. B. All rectangles are parallelograms. C. All parallelograms are rectangles. D. All quadrilaterals are squares. Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 54. A student is given the following information and then asked to write a paragraph proof. Determine which statement would correctly complete the studentβs proof. Given: Parallelogram ππ ππ and Parallelogram ππππ Prove: β π β β π Proof: We are given Parallelogram ππ ππ and Parallelogram ππππ. Since opposite angles of a parallelogram are congruent, β π β β π and β π β β π. __________________. A. Therefore, β π β β π by the Transitive Property of Congruence. B. Therefore, β π β β π by the Transformative Property of Congruence. C. Therefore, β π β β π by the Reflective Property of Congruence. D. Therefore, β π β β π by the Reflexive Property of Congruence. 55. Archeologists use coordinate grids on their dig sites to help document where objects are found. While excavating the site of a large ancient building, archeologists find what they believe to be a wooden support beam that extended across the entire building. One end of the beam was located at the coordinate (β13, 12) and markings on the beam indicate that the midpoint of the beam was located at (2, 4). Assuming the beam is still intact, where should the archeologists begin digging to find the other end of the beam? A. (β17, 4) B. (β7.5, 4) C. (β5.5, 8) D. (17, β4) Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 2016-2017 56. Use slope or the distance formula to determine the most precise name for the figure: π΄(β1, β4), π΅(1, β1), πΆ(4, 1), π·(2, β2). A. Kite B. Rhombus C. Trapezoid D. Square 57. Find the distance between the line π¦ = 2π₯ β 3 and the point (3, β7). A. 4.5 π’πππ‘π C. 10 π’πππ‘π B. 5 π’πππ‘π D. 12.2 π’πππ‘π 58. Given points π΅ (β3,3), πΆ(3, 4), and π·(4, β2). Which of the following points must be point A in order for the quadrilateral π΄π΅πΆπ· to be a parallelogram? A. π΄(β2, β1) B. π΄(β3, β2) C. π΄(β2, β3) D. π΄(β1, β2) 59. Find the area of the polygon with vertices π΄(β8, 1), π΅(β5, 6), πΆ(4, 2), and π·(β2, β2). A. 44.5 π’πππ‘π B. 46 π’πππ‘π C. 48 π’πππ‘π D. 49.5 π’πππ‘π Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) 60. 2016-2017 A researcher finds that there are 242 bacteria evenly distributed on a 1-square inch sample of a table surface. How many bacteria would the scientist expect to find on the table top mapped below where each unit of the graph is equivalent to 1 foot? A. 7,744 ππππ‘ππππ B. 92,928 ππππ‘ππππ C. 557,568 ππππ‘ππππ D. 1,115,136 ππππ‘ππππ 61. 1 Given the lines π¦ = β 3 π₯ + 2 and π¦ = π₯ β 4, find the equation for a third line that would complete a right triangle in the coordinate plane. A. π¦ = π₯ + 4 B. π¦ = βπ₯ β 5 C. π₯ = β3 D. π¦ = β3π₯ + 5 Released 8/22/16 GEOMETRY SEMESTER 1 INSTRUCTIONAL MATERIALS 2016-2017 Courses: Geometry S1 (#2211) and Foundations in Geometry S1 (#7771) Geometry Semester 1 Instructional Materials 2016-2017 Answers 1. C 11. A 21. D 31. A 41. B 51. C 2. B 12. B 22. C 32. B 42. C 52. C 3. D 13. B 23. D 33. C 43. B 53. B 4. C 14. A 24. A 34. A 44. D 54. A 5. D 15. D 25. B 35. B 45. A 55. D 6. A 16. C 26. D 36. B 46. A 56. B 7. D 17. B 27. D 37. D 47. B 57. A 8. A 18. C 28. A 38. A 48. B 58. C 9. C 19. D 29. B 39. B 49. A 59. D 10. D 20. C 30. C 40. D 50. D 60. D 61. B Released 8/22/16