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NAME ______________________________________________ DATE
____________ PERIOD _____
Skills Practice
2-1
Practice
2-1
Make a conjecture about the next item in each sequence.
(Average)
Make a conjecture about the next item in each sequence.
1.
1.
2. 24, 21, 2, 5, 8 11
11
2
7
2
9
2
4. 22, 4, 28, 16, 232 64
3. 6, }}, 5, }}, 4 }}
Make a conjecture based on the given information. Draw a figure to illustrate
your conjecture. 5–8. Sample answers are given.
6. Point P is the midpoint of N
wQ
w.
5. Points A, B, and C are collinear,
and D is between B and C.
A
C D
NP 5 PQ
B
N
P
2. 5, 210, 15, 220 25
5. /ABC is a right angle.
6. Point S is between R and T.
##$ ⊥ BC
##$
BA
RS 1 ST 5 RT
Q
B
8. /3 > /4
R
1
3
2
3
Q
AB 5 CD and BC 5 AD.
S
R
A
B
D
C
Determine whether each conjecture is true or false. Give a counterexample for
any false conjecture.
9. Given: S, T, and U are collinear and ST 5 TU.
w.
Conjecture: T is the midpoint of w
SU
9. Given: /ABC and /CBD form a linear pair.
Conjecture: /ABC > /CBD
true
False; one of the angles could be acute and the other obtuse.
10. Given: /1 and /2 are adjacent angles.
Conjecture: /1 and /2 form a linear pair.
10. Given: w
AB
w, B
wC
w, and w
AC
w are congruent.
Conjecture: A, B, and C are collinear.
False; /1 and /2 could each measure 60°.
False; A
wB
w, B
wC
w, and A
wC
w could form a triangle.
11. Given: G
wH
w and w
JK
w form a right angle and intersect at P.
w⊥J
wK
w
Conjecture: w
GH
Glencoe Geometry
A
B
true
C
12. ALLERGIES Each spring, Rachel starts sneezing when the pear trees on her street blossom.
She reasons that she is allergic to pear trees. Find a counterexample to Rachel’s conjecture.
12. Given: /1 is complementary to /2, and /1 is complementary to /3.
Conjecture: /2 > /3
Sample answer: Rachel could be allergic to other types of plants that
blossom when the pear trees blossom.
true
Glencoe/McGraw-Hill
P
4
Determine whether each conjecture is true or false. Give a counterexample for
any false conjecture.
false; counterexample:
8. ABCD is a parallelogram.
The segments form a square.
4
11. Given: AB 1 BC 5 AC
Conjecture: AB 5 BC
T
C
7. P, Q, R, and S are noncollinear
w>w
QR
w>w
RS
w>w
SP
w.
and w
PQ
/3 and /4 are vertical angles.
S
59
Answers
Glencoe Geometry
©
Glencoe/McGraw-Hill
60
Glencoe Geometry
(Lesson 2-1)
A3
/1, /2, /3, and /4 are formed
by two intersecting lines.
4. 12, 6, 3, 1.5, 0.75 0.375
Make a conjecture based on the given information. Draw a figure to illustrate
your conjecture. 5–8. Sample answers are given.
A
7. /1, /2, /3, and /4 form four
linear pairs.
1 1
8 16
1 1
2 4
3. 22, 1, 2}}, }}, 2}} }}
Answers
A, B, C, and D are collinear.
©
____________ PERIOD _____
Inductive Reasoning and Conjecture
Inductive Reasoning and Conjecture
Lesson 2-1
Glencoe/McGraw-Hill
NAME ______________________________________________ DATE
©
Glencoe/McGraw-Hill
NAME ______________________________________________ DATE
NAME ______________________________________________ DATE
____________ PERIOD _____
Skills Practice
2-2
2-2
Logic
Practice
____________ PERIOD _____
(Average)
Logic
Use the following statements to write a compound statement for each conjunction
and disjunction. Then find its truth value.
p: 23 2 2 5 25
q: Vertical angles are congruent.
r: 2 1 8 . 10
s: The sum of the measures of complementary angles is 90°.
Use the following statements to write a compound statement for each conjunction
and disjunction. Then find its truth value.
p: 60 seconds 5 1 minute
q: Congruent supplementary angles each have a measure of 90.
r: 212 1 11 , 21
1. p ` q 60 seconds 5 1 minute and congruent supplementary angles each
have a measure of 90; true.
1. p and q 23 2 2 5 25 and vertical angles are congruent; true.
2. q ~ r Congruent supplementary angles each have a measure of 90 or
212 1 11 , 21; true.
2. p ` r 23 2 2 5 25 and 2 1 8 . 10; false.
3. ,p ~ q 60 seconds Þ 1 minute or congruent supplementary angles each
have a measure of 90; true.
4. ,p ` ,r 60 seconds Þ 1 minute and 212 1 11 $ 21; false.
is 90°; true.
90°; true.
5. p ` ,q 23 2 2 5 25 and vertical angles are not congruent; false.
Copy and complete each truth table.
5.
6.
p
q
,p
,q
,p ~ ,q
p
q
,p
,p ~ q
p ` (,p ~ q)
T
T
T
F
F
T
F
T
T
T
F
F
T
F
T
T
F
F
T
F
T
F
F
T
T
T
F
F
F
F
T
T
T
F
T
T
T
F
F
F
Copy and complete each truth table.
7.
p
q
,p
,p ` q
,(,p ` q)
T
T
T
F
F
T
F
F
F
F
T
T
F
F
T
F
T
T
F
T
8.
p
q
,q
p ~ ,q
T
T
F
T
F
T
F
T
F
F
F
T
T
T
F
T
Construct a truth table for each compound statement.
7. q ~ (p ` ,q)
Construct a truth table for each compound statement.
9. ,q ` r
8. ,q ` (,p ~ q)
p q ,q p ` ,q q ~ (p ` ,q)
p q ,p ,q ,p ~ q ,q ` (,p ~ q)
T T F
F
T
T T
F
F
T
F
T F T
T
T
T F
F
T
F
F
F T F
F
T
F T
T
F
T
F
F F T
F
F
F F
T
T
T
T
10. ,p ~ ,r
,q ,q ` r
,p ,r ,p ~ ,r
Glencoe Geometry
q
r
p
r
T
T
F
F
T
T
F
F
F
T
F
F
F
T
F
F
T
T
F
T
T
T
F
T
T
F
T
F
F
T
F
F
F
T
T
T
SCHOOL For Exercises 9 and 10, use the following
information.
The Venn diagram shows the number of students in the band
who work after school or on the weekends.
Work
After
School
5
3
Work
Weekends
17
9. How many students work after school and on weekends? 3
10. How many students work after school or on weekends? 25
©
Glencoe/McGraw-Hill
65
Glencoe Geometry
©
Glencoe/McGraw-Hill
66
Glencoe Geometry
(Lesson 2-2)
A6
6. q ~ ,r Vertical angles are congruent or 2 1 8 # 10; true.
Lesson 2-2
4. r ~ s 2 1 8 . 10 or the sum of the measures of complementary angles is
Answers
3. p or s 23 2 2 5 25 or the sum of the measures of complementary angles
©
Glencoe/McGraw-Hill
NAME ______________________________________________ DATE
2-3
NAME ______________________________________________ DATE
____________ PERIOD _____
Skills Practice
2-3
Practice
____________ PERIOD _____
(Average)
Conditional Statements
Conditional Statements
Identify the hypothesis and conclusion of each statement.
Identify the hypothesis and conclusion of each statement.
1. If you purchase a computer and do not like it, then you can return it within 30 days.
1. If 3x 1 4 5 25, then x 5 23.
H: 3x 1 4 5 25; C: x 5 23
H: you purchase a computer and do not like it;
C: you can return it within 30 days
2. If x 1 8 5 4, then x 5 24.
2. If you take a class in television broadcasting, then you will film a sporting event.
H: x 1 8 5 4; C: x 5 24
H: you take a class in television broadcasting;
C: you will film a sporting event
3. If the drama class raises $2000, then they will go on tour.
Write each statement in if-then form.
H: the drama class raises $2000; C: they will go on tour
3. “Those who do not remember the past are condemned to repeat it.” (George Santayana)
4. A polygon with four sides is a quadrilateral.
4. Adjacent angles share a common vertex and a common side.
If a polygon has four sides, then it is a quadrilateral.
If two angles are adjacent, then they share a common vertex and a
common side.
Determine the truth value of the following statement for each set of conditions.
If DVD players are on sale for less than $100, then you buy one.
If you stand for nothing, then you will fall for anything.
If an angle is acute, then its measure is less than 90.
Determine the truth value of the following statement for each set of conditions.
If you finish your homework by 5 P.M., then you go out to dinner.
Lesson 2-3
5. DVD players are on sale for $95 and you buy one. true
6. An acute angle has a measure less than 90.
6. DVD players are on sale for $100 and you do not buy one. true
7. DVD players are not on sale for under $100 and you do not buy one. true
8. Write the converse, inverse, and contrapositive of the conditional statement. Determine
whether each statement is true or false. If a statement is false, find a counterexample.
If (28) 2 . 0, then 28 . 0.
7. You finish your homework by 5 P.M. and you go out to dinner. true
Converse: If 28 . 0, then (28)2 . 0; true.
Inverse: If (28)2 # 0, then 28 # 0; true.
Contrapositive: If 28 # 0, then (28)2 # 0; false.
8. You finish your homework by 4 P.M. and you go out to dinner. true
9. You finish your homework by 5 P.M. and you do not go out to dinner. false
SUMMER CAMP For Exercises 9 and 10, use the following information.
Glencoe Geometry
10. Write the converse, inverse, and contrapositive of the conditional statement. Determine
whether each statement is true or false. If a statement is false, find a counterexample.
If 89 is divisible by 2, then 89 is an even number.
Converse: If 89 is an even number, then 89 is divisible by 2; true.
Inverse: If 89 is not divisible by 2, then 89 is not an even number; true.
Contrapositive: If 89 is not an even number, then 89 is not divisible by 2;
true.
Older campers who attend Woodland Falls Camp are expected to work. Campers who are
juniors wait on tables.
9. Write a conditional statement in if-then form.
Sample answer: If you are a junior, then you wait on tables.
10. Write the converse of your conditional statement.
If you wait on tables, then you are a junior.
©
Glencoe/McGraw-Hill
71
Answers
Glencoe Geometry
©
Glencoe/McGraw-Hill
72
Glencoe Geometry
(Lesson 2-3)
A9
5. “Those who stand for nothing fall for anything.” (Alexander Hamilton)
Answers
If you do not remember the past, then you are condemned to repeat it.
Write each statement in if-then form.