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Name _______________________________________ Date ___________________ Class __________________ Tools of Geometry Quiz Choose the best answer. Refer to the figure for Exercises 1 and 2. 1. Which represents the name of the ray whose endpoint is K and that passes through R? A RK C KS B KT D RK 2. In the diagram, how many different rays have endpoint R? F 1 H 3 G 2 J 4 8. What is the next letter in the sequence? D, H, L, P, . . . F Q H S G R J T 9. Which is the counterexample that proves the conjecture false? “If two rays have the same endpoint, then they are opposite rays.” A C B D Refer to the figure for Exercises 3 and 4. 10. Identify the hypothesis of the conditional statement “Two angles are complementary if the sum of their measures is 90 degrees.” 3. What is MP? A 1 C 4 B 2 D 5 4. What is LP? F 7.5 H 2.5 G 2.5 J 7.5 5. An angle whose measure is 70° is what type of angle? A acute C obtuse B right D straight 6. GJ bisects FGH, mFGJ (7x 9)°, and mHGJ (2x 36)°. What is mFGH? F 43° H 86° G 54° J 108° 7. An angle measuring 22° is bisected. What is the measure of the angles that are formed? A 11° C 33° B 22° D 44° F if G Two angles are complementary H the sum of their measures is 90 degrees J Two angles are complementary if the sum of their measures is 90 degrees. 11. Which conditional statement has the same truth value as this statement? “The sum of two odd numbers is even.” A If two even numbers are added, then their sum is even. B If an even and odd number are added, then their sum is even. C If two even numbers are multiplied, then their product is odd. D If two odd numbers are multiplied, then their product is even. © Houghton Mifflin Harcourt Publishing Company Holt McDougal Analytic Geometry Name _______________________________________ Date ___________________ Class __________________ Tools of Geometry Quiz continued Use the figure for Exercises 12–15. 18. Find the next item in the pattern. 2, 5, 8, 11, 14, . . . ________________________________________ 12. Name a line. 19. Show that the conjecture is false by finding a counterexample. When the letters i and e appear next to each other in a word, the letter i always comes before the letter e. ____________________________________ ________________________________________ 13. Name a segment on line n. ____________________________________ 14. Name a ray with endpoint A. 20. Identify the hypothesis and conclusion of the statement “If it is raining, then there are clouds in the sky.” ________________________________________ ____________________________________ ________________________________________ 15. Name the intersection of BC and AB. ________________________________________ ____________________________________ 16. Z is in the interior of WXY. If mWXZ 110°, and mZXY 20°, what is mWXY? ____________________________________ 17. A and B are complementary. mA 29. Find mB. 21. Given: If Lewis earns a scholarship, he can go to college. Lewis earns a scholarship. Conjecture: Lewis can go to college. Determine whether the conjecture is valid by the Law of Detachment. ________________________________________ ____________________________________ © Houghton Mifflin Harcourt Publishing Company Holt McDougal Analytic Geometry Name _______________________________________ Date ___________________ Class __________________ Algebraic and Geometric Proofs Quiz Choose the best answer. 1. Consider the related biconditional statement for the conditional statement “If Shelly lives in Texas, then she lives in the United States.” Which of the following statements is true about the related biconditional statement? A The biconditional is true because the conditional is true. B The biconditional is false because the conditional and its converse are false. C The biconditional is true because the conditional and its converse are true. D The biconditional is false because the converse of the conditional is false. 2. If r 14 9, what justifies r 23? F Transitive Property of Equality G Subtraction Property of Equality 4. If 5 2k, what justifies 2k 5? F Multiplication Property of Equality G Division Property of Equality H Symmetric Property of Equality J Reflexive Property of Equality 5. Which completes the statement? If 6x 5 and d 6x, then ______ by the Transitive Property of Equality. A d5 B x 5 6 C 6x d D x d 6 6. Which completes the statement? If RS GH, then ______ by the Symmetric Property of Congruence. F RS GH H GH RS G RS RS J RS GH 7. Given: L bisects KM ; M bisects LN. Prove: KL MN H Symmetric Property of Equality J Reflexive Property of Equality x 1 8, what justifies 2 x 1 16? 3. If A Subtraction Property of Equality B Division Property of Equality Proof: Since L bisects KM and M bisects LN, by definition of bisect, KL LM and LM MN. Then, by the ? , KL MN. Finally, KL MN by the definition of congruent segments.Which completes the proof? C Transitive Property of Equality A Common Segments Theorem D Multiplication Property of Equality B Transitive Property of Congruence C Segment Addition Postulate D Symmetric Property of Congruence © Houghton Mifflin Harcourt Publishing Company Holt McDougal Analytic Geometry Name _______________________________________ Date ___________________ Class __________________ Algebraic and Geometric Proofs Quiz continued 8. Given: 1 4 Prove: 2 3 Proof: 11. Complete the sentence “A _________ is any statement that you can prove.” Statements Reasons 1. 1 4 1. Given 2. 1 and 2 are supp., and 3 and 4 are supp. 2. Lin. Pairs Thm. 3. 2 3 3. ? Which completes the proof? F Transitive Property of Congruence G Vertical Angles Theorem H Congruent Supplements Theorem J Angle Addition Postulate 9. For the following statement, what is the “Prove” statement? If ABCD is a rhombus, then it is a parallelogram. ________________________________________ 12. What is the reason for Step 2? Statements Reasons 1. 1 2 and 2 3. 1. Given 2. m1 m2 and m2 m3. 2. 3. m1 m3 3. Trans. Prop. of 4. 1 3 4. Def. of s ? ________________________________________ ________________________________________ 13. The box is part of a flowchart proof. Identify the statement. A ABCD is a quadrilateral. B ABCD is a rhombus. C ABCD is a parallelogram. D ABCD is not a square. 10. Use the Reflexive Property of Congruence to complete the statement “A ________.” ________________________________________ 14. Write True or False. A paragraph proof is less formal than a two-column proof, so you do not need to include every step. ________________________________________ ________________________________________ © Houghton Mifflin Harcourt Publishing Company Holt McDougal Analytic Geometry
