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Integrated 2 Mini-EOC 2 Answers and Sources Multiple Choice M2.3.C Write the converse, inverse, and contrapositive of a valid proposition and determine their validity. 2,3 MC, SA Y 1. What is the contrapositive of the statement below? If a triangle is isosceles, then it has two congruent sides. A. B. C. D. If a triangle does not have two congruent sides, then it is not isosceles. If a triangle has two congruent sides, then it is isosceles. If a triangle is isosceles, then it has two congruent sides. A triangle has two congruent sides if and only if it is isosceles. Answer: A http://www.ncpublicschools.org/docs/accountability/testing/eoc/Geometry/samples/Fall2003GeometryFor mWS2.pdf M2.3.E Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle. 2 MC, SA N 2. Which of the following statements about this picture is true? A. B. C. D. mO mM mM mN mM mN mN mO Answer: B http://www.ncpublicschools.org/docs/accountability/testing/eoc/Geometry/samples/Fall2003GeometryFor mWS2.pdf Integrated 2 Mini-EOC 2 Answers and Sources M2.3.G Know, prove, and apply the Pythagorean Theorem and its converse. 1,2 MC CP I 3. Which set of numbers could be the lengths of the sides of a right triangle? A. B. C. D. {10, 24, 26} {12, 16, 30} {3, 4, 6} {4, 7, 8} Answer: A http://www.jmap.org/JMAP/RegentsExamsandQuestions/2-WordDOCs/WorksheetsByPITopic/Geometry/Informal_and_Formal_Proofs/G.G.48.PythagoreanTheorem.doc M2.3.H Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent. 1,2 MC SA I 4. A large totem pole near Kalama, Washington, is 115 ft tall. On a particular day at noon it casts a 231 ft shadow. What is the sun's angle of elevation at that time? A. 29.9° B. 63.5° C. 60.1° D. 26.5° Answer: Dhttp://www.jmap.org/JMAP/RegentsExamsandQuestions/3AdobePDFs/WorksheetsByPI/Integrated_Algebra/Algebra/Drills/PR_A.A.43.pdf M2.3.I Use the properties of special right triangles (30°–60°–90° and 45°–45°–90°) to solve problems. 5. Find the length of AD 1,2 MC CP I Integrated 2 Mini-EOC 2 Answers and Sources A. 6 2 B. 9 C. 6 3 D. 12 Answer: A http://www.doe.mass.edu/mcas/2010/release/g10math.pdf M2.3.J Know, prove, and apply basic theorems about parallelograms. 2,3 MC, CP I MC SA I 6. In parallelogram PQRS the measurers of angle P and angle R are each 146°. What is the measure of angle Q? A. 146° B. 112° C. 68° D. 34° ANSWER D M2.3.M Verify and apply properties of triangles and quadrilaterals in the coordinate plane. 7. 1,2 Determine the most precise name for the figure: A(–6, –3), B(1, 0), C(4, 7), D(–3, 4). A. kite B. rectangle C. square D. rhombus ANSWER D http://www.jmap.org/JMAP/RegentsExamsandQuestions/3AdobePDFs/WorksheetsByPI/Geometry/Coordinate_Geometry/Drills/PR_G.G.69_2.pdf M2.6.E Read and interpret diagrams, graphs, and text containing the symbols, language, and conventions of mathematics. M2.3.L Determine the coordinates of a point that is described geometrically. 2,3 SA Y 1,2 MC, CP I Integrated 2 Mini-EOC 2 Answers and Sources 8. The county planning department designs a new park in the shape of a parallelogram. They put in two diagonal walkways. What will be the coordinates of the intersection of the diagonal walkways? A. (6, 2.5) B. (5, 6.5) C. (5.5, 6) D. (6, 5.5) Answer: D http://www.ncpublicschools.org/docs/accountability/testing/eoc/Geometry/samples/Fall2003GeometryFor mWS2.pdf Completion Items M2.3.J Know, prove, and apply basic theorems about parallelograms. 2,3 MC, CP 9. Identify the best name for the quadrilateral formed by the intersection of the lines listed. 3 3 3 3 y x , y x 6 , y x 6 , y x 18 2 2 2 2 Write your answer on the line. The best name for the quadrilateral is __________________________ . ANSWER parallelogram [email protected] I Integrated 2 Mini-EOC 2 Answers and Sources M2.3.K Know, prove, and apply theorems about properties of quadrilaterals and other polygons. 2,3 MC, CP I 1,2 MC, CP I MC, SA Y 10. Complete the blank statement and reason in the flowchart proof. Given: PROE is a rhombus, SPE VOE Prove: SE EV PROE is a rhombus Given SPE VOE Given SPE VOE SEP VEO ASA Vertical Angles are congruent. Answer: SE EV CPCTC Writes “PE = OE” or equivalent Writes “A rhombus has 4 congruent sides” or equivalent M2.3.L Determine the coordinates of a point that is described geometrically. 11. Points X, Y and Z are collinear. Y is the midpoint of XZ . The coordinates of point X are (-4, 5). The coordinates of point Z are (8, -3). Determine the coordinates of point Y. Write your answer on the line. What are the coordinates of point Y? ( ____ , ____ ) Answer: (2, 1) Short Answer M2.6.B Select and apply strategies to solve problems. 3 Integrated 2 Mini-EOC 2 Answers and Sources M2.5.B Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose. 2 MC, SA I 12. An overhead view of a revolving door is shown in the accompanying diagram. Each panel is 1.5 meters wide. What is the approximate width of d, the opening from B to C? What is the approximate width of d, the opening from B to C? ( ____ , ____ ) Answer: 2.12 m http://www.jmap.org/JMAP/RegentsExamsandQuestions/2WordDOCs/WorksheetsByPITopic/Geometry/Informal_and_Formal_Proofs/G.G.48.PythagoreanTheorem.doc 2-point response: The student shows understanding of selecting and applying strategies to solve problems by doing the following: Writes 2.12 m Shows a method that leads to the solution. 1-point response: The student does one of the following: Writes 2.12 m M2.3.F Determine and prove triangle congruence and other properties of triangles. 13. In the diagram AB ≅ EB and ADB ≅ ECB Prove ΔABD ≅ ΔEBC using mathematical language and concepts. Proof: 2,3 MC, SA N Integrated 2 Mini-EOC 2 Answers and Sources 2-point response: The student shows understanding of proving triangle congruence by doing the following: Writes AB ≅ EB and ∠ADB ≅ ∠ECB (given) Writes ∠ABD ≅ ∠CBE by vertical angles, or equivalent Writes ΔABD ≅ ΔEBC by Angle-Angle-Side, or equivalent 1-point response: The student does one of the following: Writes ∠ABD ≅ ∠CBE by vertical angles, or equivalent Writes ΔABD ≅ ΔEBC by Angle-Angle-Side, or equivalent Note: Student responses may be in the form of a flow chart proof, two-column proof, or paragraph proof. Student responses should refer to the given information. Sample Answers: Proof: AB ≅ CD Given ∠ADB ≅ ∠ECB Given ∠ABD ≅ ∠CBE Vertical Angles ΔABD ≅ ΔEBC AAS Congruence Proof: AB ≅ CD and ∠ADB ≅ ∠ECB are given. ∠ABD ≅ ∠CBE and ∠ABD ≅ ∠CBE are congruent because vertical angles are congruent. Therefore, ΔABD ≅ ΔEBC by AngleAngle- Side Congruence. Shows a method that could lead to the solution.