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Topic 2 TEKS Cumulative Practice Multiple Choice Read each question. Then write the letter of the correct answer on your paper. 4.Which counterexample shows that the following conjecture is false? Every perfect square number has exactly three factors. F. The factors of 2 are 1, 2. 1.What is the second step in constructing ∠S, an angle congruent to ∠A? G. The factors of 4 are 1, 2, 4. H. The factors of 8 are 1, 2, 4, 8. J. The factors of 16 are 1, 2, 4, 8, 16. A 5.How many rays are in the next two terms in the sequence? A. C. S T hsm11gmse_02cu_t00560 S R A. 16 and 33 raysC. 17 and 34 rays B. 17 and 33 raysD. 18 and 34 rays hsm11gmse_02cu_t00561 B. D. B 6.Which of the statements could be a conclusion based hsm11gmse_02cu_t00567 on the following information? If a polygon is a pentagon, then it has one more side hsm11gmse_02cu_t00562 A R S than a quadrilateral. If a polygon has one more side C than a quadrilateral, then it has two more sides than a triangle. 2.What is the converse of the following statement? If a whole number has 0 as its last digit, then the F. If a polygon is a pentagon, then it has many sides. number is evenly divisible by 10. hsm11gmse_02cu_t00564 hsm11gmse_02cu_t00565G. If a polygon has two more sides than a F. If a number is evenly divisible by 10, then it is a quadrilateral, then it is a hexagon. whole number. H. If a polygon has more sides than a triangle, then it G. If a whole number is divisible by 10, then it is an is a pentagon. even number. J. If a polygon is a pentagon, then it has two more H. If a whole number is evenly divisible by 10, then it sides than a triangle. has 0 as its last digit. 7.Which pair of angles must be congruent? J. If a whole number has 0 as its last digit, then it must A. supplementary angles be evenly divisible by 10. 3.The sum of the measures of the complement and the supplement of ∠Y is 114. What is m∠Y ? A. 12C. 78 B. complementary angles C. adjacent angles D. vertical angles B. 66D. 102 PearsonTEXAS.com 83 8.Which of the following best defines a postulate? 13. Which is an undefined term? F. a statement accepted without proof A. rayC. line G. a conclusion reached using inductive reasoning B. segmentD. intersection H. an example that proves a conjecture false J. a statement that you prove true 9.Which type of reasoning is based on patterns you observe? A. deductive reasoning B. inductive reasoning C. detachment and syllogism D. conclusion and hypothesis 10. Which property says that if a = b, then b = a? F. Reflexive Property 14. Write the following statement as a true biconditional if possible. Complementary angles are two angles with measures that have a sum of 90. F. Two angles are complementary if and only if the measures of the angles have a sum of 90. G. Two angles with measures that have a sum of 90 are complementary angles. H. Two angles with measures that do not have a sum of 90 are not complementary angles. J. not reversible 15. What is the value of x? G. Symmetric Property A. 120C. 30 H. Transitive Property (x + 90)° 4x° B. 60D. 20 J. Substitution Property 11. Which of the following is not a postulate? A. Through any three noncollinear points there is exactly one plane. B. If two distinct lines intersect, then they intersect in exactly one point. F. A figure is a hexagon if and only if it is a six-sided polygon. C. Vertical angles are congruent. G. A figure is a polygon if and only if it is a six-sided hexagon. D. Through any two points there is exactly one line. 12. When constructing a perpendicular bisector, what is the final step of the construction, after you’ve drawn two arcs, as shown here? X A B Y F. Draw a line through points A and X. G. Draw a line through points A and B. H. Draw a line through points X and B. J. Draw a line through points X and Y. 84 16. Which is the biconditional of the given statement? A hexagon is a six-sided polygon. Topic 2 TEKS Cumulative Practice H. A six-sided polygon is a hexagon. J. A hexagon is a polygon if and only if it is a six-sided figure. 17. Given the statements below, what conclusion can be made using the Law of Detachment? If a student wants to go to college, then the student must study hard. Rashid wants to go to Rice University. A. Rashid will go to Rice University. B. Rashid will not have to study hard. C. College students study hard. D. Rashid must study hard. 18. What are two pairs of congruent angles in this figure? 11111 * 11111 = 1 11111 * 11111 = 121 11111 * 11111 = 12321 11111 * 11111 = 1234321 11111 * 11111 = ■ F E I G H F. ∠EIF ≅ ∠FIG and ∠FIG ≅ ∠GIH G. ∠EIF ≅ ∠GIH and ∠EIG ≅ ∠FIH H. ∠HIG ≅ ∠EIF and ∠FIG ≅ ∠GIH J. ∠HIG ≅ ∠EIF and ∠FIH ≅ ∠GIH Gridded Response 19. What is the next number in the pattern? Constructed Response 24. On a number line, P is at -4 and R is at 8. What is the coordinate of the point Q, which is 34 the way from R to P? Show your work. 25. Write the converse, inverse, and contrapositive of the following statement. Determine the truth value of each. If you live in Oregon, then you live in the United States. 1, -4, 9, -16, c 20. m∠BZD = 107 m∠FZE = 2x + 5 m∠CZD = x What is the measure of ∠CZD ? 26. Determine the truth value of the conjecture below. If false, provide a counterexample. A perpendicular bisector of a line segment forms three pairs of vertical angles. B 27. The sequence below lists the first eight powers of 7. 71, 72, 73, 74, 75, 76, 77, 78, . . . C A D Z F E a.Make a table that lists the digit in the ones place for each of the first eight powers of 7. For example, 74 = 2401. The digit 1 is in the ones place. b.What digit is in the ones place of 734 ? Explain your reasoning. 21. The measure of an angle is three more than twice its supplement. What is the measure of the angle? 22. What is the value of x? geom12_se_ccs_c02_csr_c02.ai 3x 5 23. Continue the pattern. (2x 70) hsm11gmse_02cu_t00572 28. Write a proof. Given: ∠1 and ∠2 are supplementary. Prove: ∠1 and ∠2 are right angles. 1 2 hsm11gmse_02cu_t00573 PearsonTEXAS.com 85