VOCABULARYWhat type of statements are either both true or both false?

Luca A.

Numerade Educator

WHICH ONE DOESN'T BELONg Which statement does not belong with the other three? Explain your reasoning.

Kashif Q.

Numerade Educator

In Exercises $3-6,$ copy the conditional statement. Underline the hypothesis and circle the conclusion.

If a polygon is a pentagon, then it has ve sides.

Luca A.

Numerade Educator

In Exercises $3-6,$ copy the conditional statement. Underline the hypothesis and circle the conclusion.

If two lines form vertical angles, then they intersect.

Kashif Q.

Numerade Educator

In Exercises $3-6,$ copy the conditional statement. Underline the hypothesis and circle the conclusion.

If you run, then you are fast.

Luca A.

Numerade Educator

In Exercises $3-6,$ copy the conditional statement. Underline the hypothesis and circle the conclusion.

If you like math, then you like science.

Kashif Q.

Numerade Educator

In Exercises $7-12$ , rewrite the conditional statement in if-then form. (See Example 1.)

$9 x | 5=23,$ because $x=2$

Luca A.

Numerade Educator

In Exercises $7-12$ , rewrite the conditional statement in if-then form. (See Example 1.)

Today is Friday, and tomorrow is the weekend.

Kashif Q.

Numerade Educator

In Exercises $7-12$ , rewrite the conditional statement in if-then form. (See Example 1.)

You are in a band, and you play the drums.

Luca A.

Numerade Educator

In Exercises $7-12$ , rewrite the conditional statement in if-then form. (See Example 1.)

Two right angles are supplementary angles.

Kashif Q.

Numerade Educator

In Exercises $7-12$ , rewrite the conditional statement in if-then form. (See Example 1.)

Only people who are registered are allowed to vote.

Luca A.

Numerade Educator

In Exercises $7-12$ , rewrite the conditional statement in if-then form. (See Example 1.)

The measures of complementary angles sum to $90^{\circ} .$

Kashif Q.

Numerade Educator

In Exercises $13-16,$ write the negation of the statement.

The sky is blue.

Luca A.

Numerade Educator

In Exercises $13-16,$ write the negation of the statement.

The lake is cold.

Kashif Q.

Numerade Educator

In Exercises $13-16,$ write the negation of the statement.

The ball is not pink.

Luca A.

Numerade Educator

In Exercises $13-16,$ write the negation of the statement.

The dog is not a Lab.

Kashif Q.

Numerade Educator

In Exercises $17-24,$ write the conditional statement $p \rightarrow q,$ the converse $q \rightarrow p,$ the inverse $\sim p \rightarrow \sim q$ , and the contrapositive $\quad \mathrm{q} \rightarrow \sim \mathrm{p}$ in words. Then decide whether each statement is true or false.

Let p be "two angles are supplementary" and let q be "the measures of the angles sum to $180^{\circ}$ .

Luca A.

Numerade Educator

In Exercises $17-24,$ write the conditional statement $p \rightarrow q,$ the converse $q \rightarrow p,$ the inverse $\sim p \rightarrow \sim q$ , and the contrapositive $\quad \mathrm{q} \rightarrow \sim \mathrm{p}$ in words. Then decide whether each statement is true or false.

Let $\mathrm{p}$ be "you are in math class" and let $\mathrm{q}$ be "you are in Geometry."

Kashif Q.

Numerade Educator

In Exercises $17-24,$ write the conditional statement $p \rightarrow q,$ the converse $q \rightarrow p,$ the inverse $\sim p \rightarrow \sim q$ , and the contrapositive $\quad \mathrm{q} \rightarrow \sim \mathrm{p}$ in words. Then decide whether each statement is true or false.

Let p be "you do your math homework" and let q be "you will do well on the test."

Luca A.

Numerade Educator

In Exercises $17-24,$ write the conditional statement $p \rightarrow q,$ the converse $q \rightarrow p,$ the inverse $\sim p \rightarrow \sim q$ , and the contrapositive $\quad \mathrm{q} \rightarrow \sim \mathrm{p}$ in words. Then decide whether each statement is true or false.

Let p be "you are not an only child" and let $q$ be "you have a sibling.

Kashif Q.

Numerade Educator

Let p be "it does not snow" and let $\mathrm{q}$ be "I will run outside."

Luca A.

Numerade Educator

Let p be "the Sun is out" and let $\mathrm{qe}$ "it is daytime."

Kashif Q.

Numerade Educator

Let p be $" 3 x-7=20 "$ and let $q$ be $^{\prime} x=9 "$

Luca A.

Numerade Educator

Let p be "it is Valentine's Day" and let q be "it is February.

Kashif Q.

Numerade Educator

In Exercises $25-28,$ decide whether the statement about the diagram is true. Explain your answer using the de nitions you have learned. (See Example $4 . )$

$\mathrm{m} \angle \mathrm{ABC}=90^{\circ}$

Luca A.

Numerade Educator

In Exercises $25-28,$ decide whether the statement about the diagram is true. Explain your answer using the de nitions you have learned. (See Example $4 . )$

$\mathrm{PQ}_{\perp} \mathrm{ST}$

Kashif Q.

Numerade Educator

In Exercises $25-28,$ decide whether the statement about the diagram is true. Explain your answer using the de nitions you have learned. (See Example $4 . )$

$\mathrm{m} \angle 2 \mathrm{Im} \angle 3=180^{\circ}$

Luca A.

Numerade Educator

$\mathrm{Mis}$ the midpoint of $\overline{\mathrm{AB}}$

Kashif Q.

Numerade Educator

In Exercises $29-32,$ rewrite the de nition of the term as a biconditional statement. (See Example $5 . )$

The midpoint of a segment is the point that divides the segment into two congruent segments.

Luca A.

Numerade Educator

In Exercises $29-32,$ rewrite the de nition of the term as a biconditional statement. (See Example $5 . )$

Two angles are vertical angles when their sides form two pairs of opposite rays.

Kashif Q.

Numerade Educator

In Exercises $29-32,$ rewrite the de nition of the term as a biconditional statement. (See Example $5 . )$

Adjacent angles are two angles that share a common vertex and side but have no common interior points.

Luca A.

Numerade Educator

In Exercises $29-32,$ rewrite the de nition of the term as a biconditional statement. (See Example $5 . )$

Two angles are supplementary angles when the sum of their measures is $180^{\circ} .$

Kashif Q.

Numerade Educator

In Exercises $33-36,$ rewrite the statements as a single bi conditional statement. (See Example $5 . )$

If a polygon has three sides, then it is a triangle.

If a polygon is a triangle, then it has three sides.

Luca A.

Numerade Educator

In Exercises $33-36,$ rewrite the statements as a single bi conditional statement. (See Example $5 . )$

If a polygon has four sides, then it is a quadrilateral.

If a polygon is a quadrilateral, then it has four sides.

Kashif Q.

Numerade Educator

In Exercises $33-36,$ rewrite the statements as a single bi conditional statement. (See Example $5 . )$

If an angle is a right angle, then it measures $90^{\circ} .$

If an angle measures $90^{\circ},$ then it is a right angle.

Luca A.

Numerade Educator

In Exercises $33-36,$ rewrite the statements as a single bi conditional statement. (See Example $5 . )$

If an angle is obtuse, then it has a measure between $90^{\circ}$ and $180^{\circ}$ .

If an angle has a measure between $90^{\circ}$ and $180^{\circ},$ then it is obtuse.

Kashif Q.

Numerade Educator

ERROR ANALYSISDescribe and correct the error in rewriting the conditional statement in if-then form.

Luca A.

Numerade Educator

ERROR ANALYSISDescribe and correct the error in writing the converse of the conditional statement.

Kashif Q.

Numerade Educator

In Exercises $39-44$ , create a truth table for the logical statement. (See Example $6 .$ )

$$

\sim p \rightarrow q

$$

Luca A.

Numerade Educator

In Exercises $39-44$ , create a truth table for the logical statement. (See Example $6 .$ )

$$

\sim q \rightarrow p

$$

Kashif Q.

Numerade Educator

In Exercises $39-44$ , create a truth table for the logical statement. (See Example $6 .$ )

$$

\sim(\sim p \rightarrow \sim q)

$$

Luca A.

Numerade Educator

In Exercises $39-44$ , create a truth table for the logical statement. (See Example $6 .$ )

$$

\sim(p \rightarrow \sim q)

$$

Kashif Q.

Numerade Educator

In Exercises $39-44$ , create a truth table for the logical statement. (See Example $6 .$ )

$$

q \rightarrow \sim p

$$

Luca A.

Numerade Educator

In Exercises $39-44$ , create a truth table for the logical statement. (See Example $6 .$ )

$$

\sim(\mathrm{q} \rightarrow \mathrm{p})

$$

Kashif Q.

Numerade Educator

UsING STRUCTURThe statements below describe three ways that rocks are formed.

Luca A.

Numerade Educator

MAKING AN ARGUMEN Your friend claims the statement "If I bought a shirt, then I went to the mall"

can be written as a true biconditional statement. Your sister says you cannot write it as a biconditional. Who is correct? Explain your reasoning.

Kashif Q.

Numerade Educator

REASONING You are told that the contrapositive of a statement is true. Will that help you determine

whether the statement can be written as a true biconditional statement? Explain your reasoning.

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PROBLEM SOLVINGJe the conditional statement to identify the if-then statement as the converse, inverse, or contrapositive of the conditional statement. Then use the symbols to represent both statements.

Kashif Q.

Numerade Educator

USING STRUCTURE Exercises $49-52,$ rewrite the conditional statement in if-then form. Then underline the hypothesis and circle the conclusion.

If you tell the truth,

you don'thave to

remember anything.

Mark Twain

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USING STRUCTURE Exercises $49-52,$ rewrite the conditional statement in if-then form. Then underline the hypothesis and circle the conclusion.

You have to expect things of yourself before you can do them.Michael Jordan

Kashif Q.

Numerade Educator

USING STRUCTURE Exercises $49-52,$ rewrite the conditional statement in if-then form. Then underline the hypothesis and circle the conclusion.

If one is lucky, a solitary fantasy can totally transform one million realities. Maya Angelou

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Whoever is happy will make others happy too. Anne Frank

Kashif Q.

Numerade Educator

MATHEMATICAL CONNECTION on the statement "If $x^{2}-10=x | 2,$ then $x=4 "$ be combined with

its converse to form a true biconditional statement?

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CRITICAL THINKING The largest natural arch in the United States is Landscape Arch, located in

Thompson, Utah. It spans 290 feet.

a. Use the information to write at least two true conditional statements.

b. Which type of related conditional statement must also be true? Write the related conditional statements.

.c.What are the other two types of related conditional statements. Write the related conditional

statements. Then determine their truth values. Explain your reasoning.

Kashif Q.

Numerade Educator

REASONING Which statement has the same meaninig as the given statement?

A If you do your homework, then you can watch a movie afterward.

B If you do not do your homework, then you can watch a movie afterward.

C If you cannot watch a movie afterward, then do your homework.

D If you can watch a movie afterward, then do not do your homework.

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THOUGHT PROVOKINGWrite three conditional statements, where one is always true, one is always

false, and one depends on the person interpreting the statement.

Kashif Q.

Numerade Educator

CRITICAL THINKING one example of a conditional statement involving dates is "If today is August 31 ,

then tomorrow is September $1 .$ "Write a conditional statement using dates from two different months so that the truth value depends on when the statement is read.

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HOW DO YOU SEE IT The Venn diagram represents all the musicians at a high school. Write three

conditional statements in if-then form describing the relationships between the various groups

of musicians.

Kashif Q.

Numerade Educator

MULTIPLE REPRESENTATIONSEate a Venn diagram representing each conditional statement. Write

the converse of each conditional statement. Then determine whether each conditional statement and its

converse are true or false. Explain your reasoning.

a. If you go to the zoo to see a lion, then you will see a cat.

b. If you play a sport, then you wear a helmet.

c. If this month has 31 days, then it is not February.

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DRAWING CONCLUSIONS Of measure the heights of your classmates to get a data set.

a. Tell whether this statement is true: If $x$ and $y$ are the least and greatest values in your data set, then the mean of the data is between $x$ and $y$ .

b. Write the converse of the statement in part (a). Is the converse true? Explain your reasoning.

c. Copy and complete the statement below using mean, median, or mode to make a conditional

statement that is true for any data set. Explain your reasoning.

Kashif Q.

Numerade Educator

WRITING Write a conditional statement that is true, but its converse is false.

Shana P.

Numerade Educator

CRITICAL THINKING ON Write a series of if then statements that allow you to I nd the measure of each angle, given that $\mathrm{m} \angle 1=90^{\circ} .$ Use the de nition of linear pairs.

Kashif Q.

Numerade Educator

WRITINGAdvertising slogans such as "Buy these shoes! They will make you a better athlete!" often

imply conditional statements. Find an advertisement or write your own slogan. Then write it as a

conditional statement.

Michael H.

Numerade Educator

Find the pattern. Then draw the next two figures in the in the sequence.

Kashif Q.

Numerade Educator

Find the pattern. Then draw the next two figures in the in the sequence.

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Find the pattern. Then write the next two numbers.

$$

1,3,5,7, \dots

$$

Kashif Q.

Numerade Educator

Find the pattern. Then write the next two numbers.

$$

12,23,34,45, \dots

$$

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Find the pattern. Then write the next two numbers.

$$

2, \frac{4}{3}, \frac{8}{9}, \frac{16}{27}, \dots

$$

Kashif Q.

Numerade Educator