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Geometry Solution Manual | Reference Guide Unit 2 | Compound Statements and Indirect Proof Compound Statements and Indirect Proof Solutions 1. A. A triangle has three vertices and a rectangle has five angles. B. False; a rectangle does not have five angles. A conjunction is only true when both parts are true. Otherwise it is false. 11. A. Three is a prime number or four is a perfect square. B. True 12. A. Every square is a rhombus or every triangle has three sides. B. True 2. A. All squares are rectangles and all equilateral triangles are isosceles triangles. B. True 13. A. A triangle can have two acute angles or a triangle can have three acute angles. B. True 3. A. All squares are parallelograms and all triangles are isosceles. B. False; some triangles are not isosceles. 14. A. Three is a prime number or four is a perfect square. B. True 4. A. Five is a prime number and two is an even integer. B. True 15. A. Five is a composite number or nine is a prime number. B. False; five is not composite and nine is not prime. 5. A. All squares are rectangles and a yard is 3 feet long. B. True 16. A. Every rhombus is a square or all three-sided polygons are triangles. B. True 6. A. A triangle is a polygon and a hexagon has three sides. B. False; a hexagon does not have three sides. A conjunction is only true when both parts are true. Otherwise, it is false. 7. A. All squares are rectangles and all triangles are isosceles. B. False; some triangles are not isosceles. A conjunction is only true when both parts are true. Otherwise, it is false. 8. A. Three is a prime number and four is a perfect square. B. True 9. A. A triangle has four vertices or a rectangle has four angles. B. True. 10. A. All rectangles are squares or all isosceles triangles are equilateral triangles. B. False; some rectangles are not squares and some isosceles triangles are not equilateral. © 2009 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. 17. Disjunction 18. Conjunction 19. Conjunction 20. Disjunction 21. Conjunction 22. Disjunction 23. Exclusive or 24. Inclusive or 25. Exclusive or 26. and p T T F F q T F T F p∧q T F F F 1 of 2 Geometry Solution Manual | Reference Guide Unit 2 | Compound Statements and Indirect Proof 27. or p T T F F 28. 29. q T F T F p∨q T T T F ___› SD bisects ∠ NSB and the measures of ∠ NSD and ∠ DSB are equal. ___› SD bisects ∠ NSB or the measures of ∠ NSD and ∠ DSB are equal. ___› 30. If SD bisects ∠ NSB, then the measures of ∠ NSD and ∠ DSB are equal. ___› 31. If SD does not bisect ∠ NSB, then the measures of ∠ NSD and ∠ DSB are not equal. 32. A. Assume the quadrilateral is not a rectangle. B. The quadrilateral will not have four right angles. A square has four right angles, so this is a contradiction. C. If a quadrilateral is a square, then the quadrilateral is a rectangle. 33. A. Assume 2(10x + 3) = 5(4x − 3). B. 2(10x + 3) = 5(4x − 3) 20x + 6 = 20x − 15 6 = −15 The last statement is a contradiction. C. 2(10x + 3) ≠ 5(4x − 3) © 2009 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. 34. A. Assume the quadrilateral is not a parallelogram. B. The quadrilateral will not have two pairs of parallel sides. A rectangle has two pairs of opposite sides parallel, so this is a contradiction. C. If a quadrilateral is a rectangle, then the quadrilateral is a parallelogram. 35. Answers will vary. Sample answer: One counterexample is 12. The number 12 is divisible by 3, but it is even. 36. The value of x could be −6; (−6)2 = 36. 37. Answers will vary. Sample answer: All rectangles have four 90° angles, yet many rectangles are not square. For example, a rectangle with length 4 centimeters and width 9 centimeters is not a square. 38. Answers will vary. Sample answer: The number −2 is an integer but is not a whole number. 39. The value of n could be equal to −9; (−9)2 = 81 as well. 40. It is possible to have a parallelogram with no right angles. 41. The number 2 is a prime number, yet it is an even number. 2 of 2