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Name
SECTION
Date
Class
Ready to Go On? Quiz
2A
2-1
Using Inductive Reasoning to Make Conjectures
Find the next term in each pattern.
1. 17, 13, 9, …
2. Mon, Wed, Fri, …
6,…
2 , __
4 , __
3. __
7 9 11
4.
,
5. A biologist recorded the following data about the weight of
baby giraffes in a wildlife park. Use the table to make a
conjecture about the average weight of a baby giraffe.
6. Show that the conjecture “If a number is a
prime number, then it is an odd number” is
false by finding a counterexample.
,
,...
ID
Number
Weight
(pounds)
FR0504F
146
FR0610M
155
FR0612F
147
FR0615F
152
FR0626M
150
2-2 Conditional Statements
7. Identify the hypothesis and conclusion of the conditional statement “Two angles
are supplementary angles if the sum of their measures is 1808.”
Write a conditional statement from each of the following.
8. Sixteen-year-olds are eligible to drive.
Reptile
9.
Snake
10. The sides of a square are congruent.
Determine if each conditional is true. If false, give a counterexample.
11. If an angle is obtuse, then it has a measure of 1508.
12. If 5x 2 3 5 8x 2 15, then x 5 4.
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All rights reserved.
.
20
Holt Geometry
Name
SECTION
Date
Class
Ready to Go On? Quiz continued
2A
13. Write the converse, inverse, and contrapositive of the statement “If a ray divides
an angle into two congruent angles, then it is an angle bisector.” Find the truth
value of each.
converse
Truth value?
inverse
Truth value?
contrapositive
Truth value?
2-3 Using Deductive Reasoning to Verify Conjectures
14. Determine if the following conjecture is valid by the Law of Detachment.
Given: If Ron finishes washing the dishes, he can go to the batting cage. Ron
finishes washing the dishes.
Conjecture: Ron goes to the batting cage.
15. Determine if the following conjecture is valid by the Law of Syllogism.
Given: If two angles lie in the same plane and have a common
vertex and a common side, but no common interior points, then
they are adjacent angles. If two adjacent angles are a linear pair
then their noncommon sides are opposite rays.
Conjecture: If two angles lie in the same plane and
have a common vertex and a common side and no common
interior points, then their noncommon sides are opposite rays.
Biconditional Statements and Definitions
16. For the conditional, “If a point divides a segment into two congruent segments, then the
point is the midpoint of the segment,” write the converse and a biconditional statement.
Converse
Biconditional statement
17. Determine if the biconditional, “A number is divisible by 6 if and only if it is
divisible by 3” is true. If false, give a counterexample.
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All rights reserved.
21
Holt Geometry
Name
Date
SECTION
Class
Ready to Go On? Quiz
2B
2-5
Algebraic Proof
Solve each equation. Write a justification for each step.
1. t 2 9 5 17
b 5 24
3. __
6
2. 4m 1 7 5 23
Identify the property that justifies each statement.
4. /5 > /6, so /6 > /5
_
5. m/1 5 m/B and m/B 5 538
so m/1 5 538
_
6. JK > JK
7. x 5 5, so 5 5 x
2-6 Geometric Proof
1
2
8. Fill in the blanks to complete the two-column proof.
Given: m/1 1 m/2 5 908, m/2 1 m/3 5 908
3
Prove: m/1 5 m/3
Proof:
Statements
Reasons
1.
1. Given
2. /1 and /2 are complementary.
/2 and /3 are complementary.
2.
3.
3. > Comp. Thm.
4.
4. Def. of congruence
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All rights reserved.
26
Holt Geometry
Name
Date
SECTION
Class
Ready to Go On? Quiz continued
2B
9. Use the given plan to write a two-column proof.
___›
___›
Q
Given: PR bisects /QPS. PS bisects /RPT.
Prove: m/1 5 m/3
Plan: By the definition of angle bisectors, /1 > /2 and /2 > /3.
Use the Transitive Property of Congruence to show that /1 > /3.
1
P
R
2
3
S
Use the definition of congruent angles to show that m/1 5 m/3.
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
2-7
T
1
Flowchart and Paragraph Proofs
2
Use the given two-column proof to write the following.
3
Given: /1 > /3
Prove: m/2 1 m/3 5 1808
Statements
Reasons
1. /1 > /3
1. Given
2. m/1 5 m/3
2. Def. of > /s
3. /1 and /2 are supplementary.
3. Lin. Pair Thm.
4. m/1 1 m/2 5 1808
4. Def. of supp. /s
5. m/3 1 m/2 5 1808
5. Subs. Prop. Of Equality
10. a flowchart proof
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All rights reserved.
11. a paragraph proof
27
Holt Geometry
Name
SECTION
Date
Class
Ready to Go On? Enrichment
2B
Proofs
Write a two-column proof.
1. Given: /2 and /3 are supplementary; /3 > /4
Prove: /1 and /5 are supplementary.
3
1 2
4 5
6
Statements
Reasons
1. /2 and /3 are supp., /3 > /4
1. Given
2.
2.
3.
3.
4.
4.
5.
5.
6.
6.
7.
7.
8. /1 and /5 are supplementary.
8.
1
2. Given: m/1 1 m/2 1 m/3 5 1808
Prove: m/1 1 m/2 5 m/4
2
3
Statements
Reasons
1.
1.
2.
2.
3.
3.
4.
4.
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All rights reserved.
4
28
Holt Geometry