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13. Persevere in solving problems. Use this picture pattern.
a. Draw the next two shapes in the pattern.
b. What numbers represent the next three figures in the pattern?
c. Verbally describe the pattern of the sequence.
d. How many dots are added from the first diagram to the second? From the second diagram to the third? From the third to the fourth? Explain how to find the nth term.
14. Which rule describes how to find the next term in the sequence?
0, 3, 9, 21, 45, 93, . . .
A. Multiply the previous term by 3.
B. Add 3 to the previous term, and then multiply the result by 3.
C. Multiply the previous term by 2, and then add 3.
D. Divide the previous term by 3, and then add 3.
15. Construct viable arguments. Explain how you knew that the rules you did not choose in Item 14 were incorrect.
LeSSon 2-2 16. Use expressions for even integers to show that the
product of two even integers is an even integer.
17. Consider these true statements.
• Allglassobjectsarebreakable.
• Allwindshieldsaremadeofglass.
• Tonette’scarhasawindshield.
Based on deductive reasoning, which of the following statements is not necessarily true?
18. Make use of structure. Use deductive reasoning to prove that x 5 5 is not in the solution set of the inequality 2x 1 1 , 7. Be sure to justify each step in your proof.
19. During the first month of school, students recorded each day on which they had a quiz in math class. A student stated that there is a math quizeveryTuesdaymorning.Isthestudent’sstatement a conjecture or a theorem? Explain.
20. Reason abstractly. A student knows that (1) any two diameters in a circle bisect each other and (2) RS and TV are two different diameters in the same circle. The student concludes that RS and TV bisect each other.
a. Is this an example of inductive or deductive reasoning? Explain.
b. Is the conclusion correct? Support your answer.
LeSSon 3-1 21. Make use of structure. In each statement, tell
whether each bold term is undefined or defined.
a. An angle is formed by two rays that have a common endpoint.
b. A line segment consists of two points and all the points between them.
c. A triangle is the union of three segments that intersect at their endpoints.
d. If two lines intersect, then there is exactly one plane that contains the two lines.
28. Suppose that this statement is true: If I wear boots or a raincoat, then I carry an umbrella. Also suppose that the hypothesis of that statement is true. Which statement must also be true?
A. I am wearing boots.
B. I am not wearing a raincoat.
C. I am not carrying an umbrella.
D. I am carrying an umbrella.
29. Write a true conditional statement that includes
this hypothesis: x3 18
21
5 .
30. Model with mathematics. Write a two-column proof to prove that your conditional statement in Item 29 is true.
Statements Reasons
1. x3 18
21
51. Given
2. a. 2. b.3. c. 3. d.4. e. 4. Division (or Multiplication)
Property of Equality
LeSSon 3-3
31. Write the inverse and the contrapositive of each statement.
a. If it is raining, then I stay indoors.
b. If I have a hammer, then I hammer in the morning.
32. Write the following biconditional statement as two conditional statements:
People have the same ZIP code if and only if they live in the same neighborhood.
33. Make use of structure. Use this statement: If 3x 5 0, then x fi 0.
a. Is the statement true? Explain.
b. Write the converse of the statement, and explain whether or not the converse is true.
c. Write the inverse of the statement, and explain whether or not the inverse is true.
d. Write the contrapositive of the statement, and explain whether or not the contrapositive is true.
34. Which two forms of a conditional statement always have the same truth value?
A. statement and inverse
B. inverse and contrapositive
C. converse and contrapositive
D. converse and inverse
35. Reason abstractly. Use this statement: If two lines form equal adjacent angles, then the lines are perpendicular. Then tell whether each statement is the inverse, converse, or contrapositive of the original statement.
a. If two lines are not perpendicular, then they do not form equal adjacent angles.
b. If two lines do not form equal adjacent angles, then they are not perpendicular.
LeSSon 4-1 36. Suppose point T is between points R and V on a
line. If RT 5 6.3 units and RV 5 13.1 units, then what is TV?
A. 2.5 units
B. 6.8 units
C. 7.8 units
D. 19.4 units
37. Suppose P is between M and N.
a. If MN 5 10, MP 5 x 2 1, and PN 5 x 1 1, what is the value of x?
b. If PM 5 2x 2 5, PN 5 6x, and MN 5 5x 1 4, what is the value of x?
38. Attend to precision. Use the centimeter ruler shown.
14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
R W
a. What is the length of RW?
b. What number on the ruler represents the midpoint of RW?
c. Suppose Q is a point on RW� ���
. If QW 5 12, what are the possible coordinates of point Q?
d. Suppose point T is between points R and W and RTTW
12
5 . What is the length of RT?
39. Reason quantitatively. On a number line, the coordinate of point A is negative and the coordinate of point B is positive.
a. When will the midpoint of AB be positive?
b. When will the midpoint of AB be negative?
c. When will the midpoint of AB be zero?
d. When will the distance from A to B be negative?
50. Model with mathematics. Every point on a circle is the same distance from the center of the circle. If (x, y) represents any point on a circle and (5, 2) is the center of the circle, use the Distance Formula to represent the length of the radius r of the circle.
LeSSon 5-2 51. Model with mathematics. BC has endpoints
B(23, 25) and C(12, 12). Find the coordinates of the midpoint of BC .
52. In the diagram shown, points S and T are the midpoints of PQ and PR, respectively.
b. Which of the points, B, M, or C, is closest to A?
54. Which expression represents the midpoint of the line segment with endpoints (x, y) and (p, q)?
A.
x y p q2
,2
1 1
B.
x p y q2
,2
2 2
C.
x p y q2
,2
1 1
D.
xp yq2,2
55. For the coordinates (5, 8) and (9, 14), one is an endpoint of a line segment and the other is the midpoint. How many possibilities are there for the other endpoint? Find each one. Explain your method.
LeSSon 6-1 56. Construct viable arguments. Use the diagram
shown.
TC
A
B
1
2
Write a statement that can be justified by each of the following:
69. Attend to precision. Suppose that ∠1 and ∠2 are same-side interior angles formed by two parallel lines cut by a transversal, and that m∠1 5 7x 2 4 and m∠2 5 20x 2 5.
a. What is the value of x?
b. What is m∠1?
c. What is m∠2?
d. Explain how you found your answers.
70. Complete the proof that if parallel lines are cut by a transversal, then same-side exterior angles are supplementary.
1 2m
n
t
43
5 687
Given: m || n
Prove: m∠7 1 m∠1 5 180
Statements Reasons
1. m || n 1. a.
2. ∠3 > ∠7, ∠1 > ∠5 2. b.
3. m∠3 5 m∠7, m∠1 5 m∠5
3. If two angles are congruent, then they have the same measure.
4. m∠3 1 m∠5 5 180 4. c.5. d. 5. Substitution
Property of Equality
LeSSon 7-2 71. Use the diagram shown.
1 2 m
n
t
43
5 687
a. Suppose m∠5 5 130°. What is m∠3 so that m || n?
b. Suppose m∠8 5 141°. What is m∠4 so that m || n?
c. Suppose m∠3 5 42°. What is m∠6 so that m || n?
d. Suppose m∠7 5 37°. What is m∠1 so that m || n?
72. Use the diagram shown.
1 2 m
n
t
43
5 687
Suppose m∠3 5 5x 1 11 and m∠5 5 16x 1 1. What must the value of x be in order for line m to be parallel to line n?
80. express regularity in repeated reasoning. In this diagram, AT 5 2x 1 3, CT 5 3x 2 1, BT 5 x 1 5, DT 5 4x 1 1, and m∠ATD 5 41x 1 8. If x 5 2, which segment is the perpendicular bisector of the other? Explain your reasoning.
A
T
B
C
D
LeSSon 8-1 81. Attend to precision. Use the ordered pairs A(3, 7),
B(22, 4), C(0, 5), and D(10, 0).
a. Find the slope of AB.
b. Find the slope of CD.
c. Find the slope of any line parallel to BC .
d. Find the slope of any line perpendicular to AD.
82. Use the three ordered pairs X(1, 0), Y(10, 3), and Z(15, 4). Which of the following statements CANNOT be true?
A. There is a line through Z that is parallel to XY� ���
.
B. There is a line through Z that is perpendicular to XY� ���
.
C. There is a line through Z that is the same line as XY� ���
.
D. There is a line through Z that intersects XY� ���
.
83. MN� ����
has a slope of 45
and PQ� ���
has a slope of 45
2 .
Are the lines parallel, perpendicular, or neither? Justify your answer.
84. � ���PQ contains the two points (0, 3) and (5, 27). The slope of
� ��RS is 1
2. Are the two lines parallel,
perpendicular, or neither? Justify your answer.
85. Make use of structure. For rectangle ABCD, two vertices are A(22, 3) and B(4, 6). Find the slopes of BC, CD, and DA. Explain your answer.
87. Use the two ordered pairs A(22, 9) and B(0, 1).
a. Suppose ⊥BC AB. Find the slope of � ��BC.
b. Write an equation in point-slope form for � ��BC.
c. Write an equation for � ��BC in slope-intercept
form.
d. Write an equation for � ��AB in point-slope form.
88. Which of the following is NOT an equation for a line perpendicular to y 5 2
3 x 2 1?
A. y x32
652 1
B. 3x 1 2y 5 5
C. 4y 5 26x
D. y x2 32
152 1
89. Reason abstractly. Suppose you are given two ordered pairs A and B. Explain how to write the equation of a line parallel to
� ��AB through a
given point.
90. Model with mathematics. A segment has endpoints P(24, 5) and Q(2, 21). Find the equation, in slope-intercept form, of the perpendicular bisector of PQ. Explain your solution.