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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
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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.
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