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McDougal Littell Jurgensen Geometry : Student Edition 2000

Ray C. Jurgensen, Richard G. Brown

Chapter 2

Deductive Reasoning - all with Video Answers

Educators


Section 1

If-Then Statements; Converses

00:13

Problem 1

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

Amrita Bhasin
Amrita Bhasin
Numerade Educator
00:35

Problem 2

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

DS
Dre'Shana Shoffner
Numerade Educator
00:17

Problem 3

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

Amrita Bhasin
Amrita Bhasin
Numerade Educator
00:47

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 Shoffner
Numerade Educator
00:13

Problem 5

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

Amrita Bhasin
Amrita Bhasin
Numerade Educator
00:14

Problem 6

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

Ashley High
Ashley High
Numerade Educator
00:24

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 Bhasin
Amrita Bhasin
Numerade Educator
00:59

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 $m \angle A O C=180$.

Ashley High
Ashley High
Numerade Educator
00:13

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 Bhasin
Amrita Bhasin
Numerade Educator
00:43

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.

Ashley High
Ashley High
Numerade Educator
00:25

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 Bhasin
Amrita Bhasin
Numerade Educator
01:12

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 Shoffner
Numerade Educator
00:18

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 Bhasin
Amrita Bhasin
Numerade Educator
00:51

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 $x>5$.

Ashley High
Ashley High
Numerade Educator
00:23

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.

Ashley High
Ashley High
Numerade Educator
00:22

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.

Amrita Bhasin
Amrita Bhasin
Numerade Educator
00:22

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 Bhasin
Amrita Bhasin
Numerade Educator
00:20

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 $x=-2$.

Ashley High
Ashley High
Numerade Educator
00:25

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 Bhasin
Amrita Bhasin
Numerade Educator
00:31

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.

Ashley High
Ashley High
Numerade Educator
00:22

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 Bhasin
Amrita Bhasin
Numerade Educator
00:27

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 $m \angle A=m \angle B$

Ashley High
Ashley High
Numerade Educator
00:39

Problem 23

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

Amrita Bhasin
Amrita Bhasin
Numerade Educator
00:26

Problem 24

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

Ashley High
Ashley High
Numerade Educator
00:23

Problem 25

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

Amrita Bhasin
Amrita Bhasin
Numerade Educator
00:28

Problem 26

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

Ashley High
Ashley High
Numerade Educator
00:39

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 Bhasin
Amrita Bhasin
Numerade Educator
00:43

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 $G H=2 P G$

Ashley High
Ashley High
Numerade Educator
02:31

Problem 29

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
Write a definition of congruent angles as a biconditional.

Margaret Fernandes
Margaret Fernandes
Numerade Educator
00:27

Problem 30

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
Write a definition of a right angle as a biconditional.

Ashley High
Ashley High
Numerade Educator
00:36

Problem 31

Tell whether each statement is true or false. Then write the converse and tell whether it is true or false.
What can you conclude if the following sentences are all true?
(1) If $p,$ then $q$
( 2)$p$
(3) If $q,$ then not $r$
(4) $s$ or $r$

Amy Jiang
Amy Jiang
Numerade Educator