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Name _______________________________________ Date ___________________ Class __________________ Geometric Reasoning Chapter 2 Review Circle the best answer. 1. What is the next item in the pattern? A C B D 6. Given: Three noncollinear points lie on the same plane. A student makes a three-legged stool. What conclusion can be drawn? F The stool will wobble. G The stool will fall over. H The stool will not wobble. 2. Which conjecture is NOT always true? F Intersecting lines form 4 pairs of adjacent angles. G Intersecting lines form 4 pairs of linear adjacent angles. H Intersecting lines form 4 pairs of congruent angles. J Not here 3. Given the conditional statement “The counting number 0 is an integer,” what can be concluded? A The statement is false because the hypothesis is false. B The statement is false because the conclusion is false. C The statement is false because both the hypothesis and the conclusion are false. D The statement is true. 4. Which is NOT a counterexample for the conditional statement “If x 0, then 1 x”? x 1 F 2 H 2 G 1 J 2 5. Let p represent “B is between A and C” and q represent “A, B, and C are collinear.” Which symbolic statement represents the conditional statement “If B is not between A and C, then A, B, and C are not collinear”? A pq C -p -q B qp D J No conclusion can be drawn. 7. If the number formed by the last two digits of a larger number is divisible by 4, then the larger number is divisible by 4. If a number is divisible by 4, then it is divisible by 2. What conclusion can be drawn about the numbers if its last two digits are 92? A Only the smaller number is divisible by 2. B Both numbers are divisible by 2. C Only the larger number is divisible by 2. D No conclusion can be drawn. 8. Which conditional statement can be used to write a true biconditional? F If a figure is a square, then it is a rectangle. G If the product is odd, then both factors are odd. H If two angles form a linear pair, then they are adjacent. J If two angles are supplementary, then both angles are obtuse. 9. Suppose that m1 mA, and mA 34. What can you conclude by using the Transitive Property of Equality ? A 34 mA C mA mA B mA m1 D m1 34 p -q Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry Name _______________________________________ Date ___________________ Class __________________ Chapter 2 Review continued 10. Which could NOT be used to justify 1 2? F Trans. Prop. of G Reflex. Prop. of H Sym. Prop. of J Def. of Use the partially completed twocolumn proof for Exercises 11 and 12. Use the two-column proof and partially completed flowchart proof for Exercises 13 and 14. Given: 1 and 2 are complementary and 1 3. Prove: 2 and 3 are complementary. Flowchart Proof: Given: X is in the interior of ABC, ABC is a right angle, and mXBC 45. Prove: BX bisects ABC. Proof: Statements Reasons 1. X is in the interior of ABC. 1. Given 2. 2. ? ? 3. ABC is a right angle. 3. Given 4. ? 4. ? 5. mXBC 45 5. Given 6. 6. Subst. ? 7. mABX 45 7. ? 8. 8. ? ? 9. BX bisects ABC. 9. Def. of bisector 11. Which is NOT a statement for Steps 2, 4, 6, or 7? A mABX 458 90 B mABC mABX mXBC C mABC 90 D ABX XBC 12. Which is NOT a reason for Steps 2, 6, 7, or 8? F Add. Post. G Subtr. Prop. of H Def. of rt. J Def. of ? Two-Column Proof: Statements Reasons 1. 1 and 2 are complementary. 1. Given 2. m1 m2 908 2. Def. of ? 3. 1 3 3. Given 4. m1 m3 4. Def. of 5. m2 m3 908 5. Subst. 6. 2 and 3 are complementary. 6. Def. of comp. ? 13. In the flowchart proof, what belongs in the space labeled “a”? A m3 m2 908 B 1 3 C m1 m2 908 D m1 m3 14. In the flowchart proof, what belongs in the space labeled “b”? F Def. of comp. ? G Subst. H Def. of ? J Add. Post. Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. Holt McDougal Geometry