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Reasoning Pre-Assessment Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Determine the next number in the sequence below. Is this inductive or deductive reasoning? 1, 2, 4, 7, 11... ____ A. The next number is 22. This is inductive reasoning. C. The next number is 16. This is inductive reasoning. B. The next number is 22. This is deductive reasoning. D. The next number is 16. This is deductive reasoning. 2. Use deductive reasoning to make a correct conclusion. If you are in 10th grade, then you are taking Geometry. You are in 10th grade. ____ ____ A. You are taking Geometry. C. It cannot be determined if you are taking Geometry. B. You are not taking Geometry. D. You are a sophomore. 3. Which of the following statements represents logical reasoning? A. an algebraic equation C. an observed experiment B. a doctor examining a patient D. a geometric proof 4. One axiom or postulate of Euclidean Geometry is: A. Vertical angles are congruent. B. A parrallelogram has two pair of parallel sides. ____ C. Parallel lines always have corresponding angles. D. A straight line can be drawn to connect any two points. 5. What are the undefined terms of Geometry? A. Point and line C. Point and plane B. Point, line and plane D. Point, line and circle ____ 6. Determine which conjuction below is true. A. An isosceles triangle has two congruent sides and congruent base angles. C. A scalene triangle has three noncongruent sides and three acute angles. B. An equilateral triangle has three D. An isosceles triangle has two congruent sides and three 120º angles. congruent sides and three acute angles. ____ 7. Use the statement below to determine which condition makes the disjunction false. “A quadrilateral is a parallelogram or a trapezoid” ____ ____ A. A square is a quadrilateral. C. A kite is a quadrilateral. B. A rectangle is a parallelogram. D. A trapezoid is not a parallelogram. 8. Determine which existential statement is correct. A. There exists an x, such that -x is a positive number. C. For all x, B. There exists an x, such that positive number. D. For all x, is a is a negative number. is a negative number. 9. Write a conditional statement based on the declarative: “A rhombus is a parallelogram with four equal sides.” A. If a parallelogram has right equal sides, then it is a rhombus. C. If a parallelogram is a rhombus, then it has four equal sides. B. If a rhombus has four equal sides, then D. If a rhombus is a parallelogram, then it it is a parallelogram. has four equal sides. ____ 10. Which part of the statement below is the hypothesis? “If a triangle has one right angle, then it is a right triangle.” A. A triangle is a right triangle. C. A right triangle has one right angle. B. A triangle has one right angle. D. A right triangle has two acute angles. ____ 11. What statement would you begin with if you were going to prove that alternate interior angles, and , have the same measure using a proof by contradiction? A. and angles. are not alternate interior C. B. and angles. are same-side interior D. ____ 12. When do you know you have completed a proof by contradiction? A. When there are two statements in your C. When you have used the same reason proof that are exact opposites. more than once. B. When there are two statements in your D. When you write QED. proof that are exactly the same. ____ 13. Determine which statement below is true. A. Sunlight is a necessary condition for growing food. C. Studying for a test is a necesary condition for passing the test. B. Getting all A’s in high school is a necessary condition for getting into college. D. Rain is a necessary condition to make the ground wet. ____ 14. Determine which statement below is true. A. Having two pair of congruent sides is a C. Having four congruent sides is a sufficient condition to make a sufficient condition to make a quadrilateral a kite. parallelogram a square. B. Being female is a sufficient condition to being a mother. D. Having two congruent sides is a sufficient condition to make a triangle isosceles. ____ 15. Determine which statement below is true. A. A parallelogram with four congruent C. A triangle with three acute angles is sides is necessary and sufficient to say necessary and sufficient to say the the figure is a square. triangle is equiangular. B. A rectangle with four congruent sides is necessary and sufficient to say the figure is a square. D. Two angles whose measures add up to 180º is necessary and sufficient to say the two angles form a linear pair. Use the figure and proof below for the next two questions. Given: n and m are parallel Prove: and are congruent. Statements 1. n and m are parallel 2. 3. 4. Reasons 1. Given 2. Reason A 3. parallel lines imply corresponding angles are congruent 4. Reason B ____ 16. Determine the correct reason to put in the “Reason A” spot in the proof above. A. parallel lines imply alternate interior C. vertical angles are congruent angles are congruent B. parallel lines imply that corresponding D. parallel lines imply alternate exterior angles are congruent angles are congruent ____ 17. Determine the correct reason to put in spot “Reason B” in the proof above. A. substitution property of equality C. transitive property B. parallel lines imply alternate exterior angles are congruent D. reflexive property Use the figure and proof below for the next two questions. Given: n and m are parallel Prove: and are supplementary Statements 1. line m and line n are parallel 2. 3. 4. 5. 6. and are supplementary Reasons 1. Given 2. Reason A 3. parallel lines imply corresponding angles are congruent 4. Congruent angles have the same measure. 5. Reason B 6. Definition of supplementary angles. ____ 18. Determine the correct reason for “Reason A” in the proof above. A. a linear pair has a sum of 180º B. supplementary angles have a sum of 180º C. complementary angles have a sum of 180º D. corresponding angles have a sum of 180º ____ 19. Determine the correct reason for “Reason B” in the proof above. A. transitive property C. reflexive property B. addition property of equality D. substitution property of equality Use the figure and proof below for the next three questions. Given: and Prove: 1. 2. 3. 4. Statements and 1. 2. 3. 4. Reasons Given Reason A Reason B Reason C ____ 20. Determine the correct reason for “Reason A” in the proof above. A. and are corresponding angles B. C. and are supplementary angles and are complementary D. vertical angles are congruent angles ____ 21. Determine the correct reason for “Reason B” in the proof above. A. SAS Triangle Congruence C. SSS Triangle Congruence B. ASA Triangle Congruence D. SSA Triangle Congruence ____ 22. Determine the correct reason for “Reason C” in the proof above. A. substitution property of equality C. SSS Triangle Congruence B. Corresponding Parts of Congruent Triangles are Congruent D. Corresponding Parts of Similar Triangles are Similar Use the following conditional statement for the next three questions: “If a parallelogram is a rectangle, then it has four right angles.” ____ 23. Write the converse of the conditional statement above. A. If a parallelogram has four right angles, then it is a rectangle. C. If a parallelogram is not a rectangle, then it does not have four right angles. B. If a parallelogram is a rectangle, then it D. If a parallelogram does not have four has four right angles. right angles, then it is a rectangle. ____ 24. Write the inverse of the conditional above. A. If a parallelogram is a rectangle, then it C. If a parallelogram has four right does not have four right angles. angles, then it is a rectangle. B. If a parallelogram is not a rectangle, D. If a parallelogram does not have four then it does not have four right angles. right angles, then it is not a rectangle. ____ 25. Write the contrapositive of the conditional statement above. A. If a rectangle does not have four right angles, then it is not a parallelogram. C. If a parallelogram does not have four right angles, then it is not a rectangle. B. If a rectangle is not a parallelogram, D. If a parallelogram is not a rectangle, then it does not have four right angles. then it does not have four right angles.