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Geometry

Ray C. Jurgensen,Richard G. Brown,John W. Jurgensen

Chapter 2

Deductive Reasoning

Educators

DS

Problem 1

Write the hypothesis and the conclusion of each conditional.
If $3 x-7=32,$ then $x=13$

Amrita B.
Numerade Educator

Problem 2

Write the hypothesis and the conclusion of each conditional.
I can't sleep if I'm not tired.

DS
Dre'Shana S.
Numerade Educator

Problem 3

Write the hypothesis and the conclusion of each conditional.
I'll try if you will.

Amrita B.
Numerade Educator

Problem 4

Write the hypothesis and the conclusion of each conditional.
If $m \angle 1=90,$ then $\angle 1$ is a right angle.

DS
Dre'Shana S.
Numerade Educator

Problem 5

Write the hypothesis and the conclusion of each conditional.
$a+b=a$ implies $b=0$

Amrita B.
Numerade Educator

Problem 6

Write the hypothesis and the conclusion of each conditional.
$x=-5$ only if $x^{2}=25$

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Problem 7

Rewrite each pair of conditionals as a biconditional.
If $B$ is between $A$ and $C,$ then $A B+B C=A C$ .
If $A B+B C=A C$ , then $B$ is between $A$ and $C$ .

Amrita B.
Numerade Educator

Problem 8

Rewrite each pair of conditionals as a biconditional.
If $m \angle A O C=180,$ then $\angle A O C$ is a straight angle.
If $\angle A O C$ is a straight angle, then $m \angle A O C=180$ .

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Problem 9

Write each biconditional as two conditionals that are converses of each other.
Points are collinear if and only if they all lie in one line.

Amrita B.
Numerade Educator

Problem 10

Write each biconditional as two conditionals that are converses of each other.
Points lie in one plane if and only if they are coplanar.

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Problem 11

Provide a counterexample to show that each statement is false. You may use words or a diagram.
If $a b<0,$ then $a<0$

Amrita B.
Numerade Educator

Problem 12

Provide a counterexample to show that each statement is false. You may use words or a diagram.
If $n^{2}=5 n$ . then $n=5$

DS
Dre'Shana S.
Numerade Educator

Problem 13

Provide a counterexample to show that each statement is false. You may use words or a diagram.
If point $G$ is on $\overrightarrow{A B},$ then $G$ is on $\overrightarrow{B A}$

Amrita B.
Numerade Educator

Problem 14

Provide a counterexample to show that each statement is false. You may use words or a diagram.
If $x y>5 y,$ then $x>5$

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Problem 15

Provide a counterexample to show that each statement is false. You may use words or a diagram.
If a four-sided figure has four right angles, then it has four congruent sides.

Amrita B.
Numerade Educator

Problem 16

Provide a counterexample to show that each statement is false. You may use words or a diagram.
If a four-sided figure has four congruent sides, then it has four right angles.

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Problem 17

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
If $x=-6,$ then $|x|=6$

Amrita B.
Numerade Educator

Problem 18

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
If $x^{2}=4,$ then $x=-2$

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Problem 19

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
If $b>4,$ then $5 b>20$

Amrita B.
Numerade Educator

Problem 20

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
If $m \angle T=40,$ then $\angle T$ is not obtuse.

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Problem 21

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
If Pam lives in Chicago, then she lives in Illinois.

Amrita B.
Numerade Educator

Problem 22

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
If $\angle A \cong \angle B,$ then $m \angle A=m \angle B$

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Problem 23

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
$$
a^{2}>9 \text { if } a>3
$$

Amrita B.
Numerade Educator

Problem 24

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
$$
x=1 \text { only if } x^{2}=x
$$

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Problem 25

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
$$
n>5 \text { only if } n>7
$$

Amrita B.
Numerade Educator

Problem 26

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
$$
a b=0 \text { implies that } a=0 \text { or } b=0
$$

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Problem 27

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
If points $D, E,$ and $F$ are collinear, then $D E+E F=D F$

Amrita B.
Numerade Educator

Problem 28

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
$P$ is the midpoint of $\overline{G H}$ implies that $G H=2 P G$

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Problem 29

Write a definition of congruent angles as a biconditional.

Amrita B.
Numerade Educator

Problem 30

Write a definition of a right angle as a biconditional.

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Problem 31

What can you conclude if the following sentences are all true?
$\begin{array}{llll}{\text { (1) If } p, \text { then } q .} & {\text { (2) } p} & {\text { (3) If } q, \text { then not } r .} & {\text { (4) } \operatorname{sor} r}\end{array}$

Amrita B.
Numerade Educator