Download Practice C - Elmwood Park Memorial High School

Name ________________________________________ Date __________________ Class__________________
LESSON
2-1
Practice C
Using Inductive Reasoning to Make Conjectures
Make a conjecture about each pattern. Write the next two items.
1. −1, −8, −27, −64, . . .
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2. 1, 11, 21, 1211, 111221, . . . (Hint: Try reading the numbers aloud in different ways.)
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3. A, E, F, H, I, . . .
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4.
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Determine if each conjecture is true. If not, write or draw a counterexample.
5. Three points that determine a plane also determine a triangle.
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6. An image reflected across the x-axis cannot appear identical
to its preimage.
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7. If a > b and b > c, then a − b < a − c.
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8. If n is an integer (n ≠ 0), then
3
1 ⎛ 1⎞
>⎜ ⎟ .
n ⎝ n⎠
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9. Hank finds that a convex polygon with n sides has n − 3 diagonals from any one
vertex. He notices that the diagonals from one vertex divide every polygon into
triangles, and he knows that the sum of the angle measures in any triangle is 180°.
Hank wants to develop a rule about the sum of the angle measures in a convex
polygon with n sides. Find the rule. (Hint: Sketching some polygons may help.)
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10. A regular polygon is a polygon in which all sides have the same length and all
angles have the same measure. Use your answer to Exercise 9 to determine the
measure of one angle in a regular heptagon, a regular nonagon,
and a regular dodecagon. Round to the nearest tenth of a degree. ____________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
2-5
Holt McDougal Geometry
Answers for the chapter Geometric Reasoning
2-1 USING INDUCTIVE REASONING TO
3. The pattern is the letters of the alphabet
that are made only from straight
segments; K, L.
MAKE CONJECTURES
Practice A
1. 10
4. First rotate the figure 180°. Then reflect
the figure across a vertical line. Repeat.
2. W
3. summer
5. true
6. false
4. inductive reasoning
5. true
6. even
Sample answer:
7. n
7. true
8. The number of rings in a tree is the same
as the tree’s age.
9. 82 rings
8. false
10. false
Possible answers: n = 1, n = −1
11. Possible answers: zero, any negative
number
9. Sum of angle measures = [180(n − 2)]°
10.128.6°; 140°; 150°
Reteach
1
1. 1
4
12. Possible answer:
Practice B
1. 36
2.
3. Arkansas
4. north
5. positive
6. n − 3
7. Possible answers: zero, any negative
number
2. 36
3.
4.
5. doubled
6. 2n
7. n + 2
8.
8. Possible answer: If the lines are parallel,
then they do not intersect.
9. Possible answer: If point N is between
points A and G, then AN = 2 inches.
9. One-third of the bills were counterfeit.
10. Sample answer: If x = 0 and y = −1, then
x 2 < y 2.
10. Each item, starting with the third, is the
product of the two preceding items; 256,
8192.
11. Sample answer: ∠ABD, ∠DBE, ∠EBC,
∠ABE, ∠DBC
11. The dot skips over one vertex in a
clockwise direction.
12. Sample answer: m∠1 = 25°, m∠2 = 20°
13. true
Practice C
1. The pattern is the cubes of the negative
integers; −125, −216.
14.
Challenge
1. 1, 6, 15, 20, 15, 6, 1
2. Each item describes the item before it
(one, one one, two ones, . . .); 312211,
13112221.
2. Each row has 1 as the first and last
number. Each of the other numbers is
found by adding the two numbers that
appear just above it.
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A9
Holt McDougal Geometry