Free Printable Q1,HW #23 - Biconditional Statements

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Q1,HW #23 - Biconditional Statements

Total questions: 37

Worksheet time: 3hrs 31mins

Name

Class

Date

Identify the hypothesis:

If an angle measures 90 $\degree$ , then it is a right angle.

if an angle measures 90 $\degree$

an angle measures 90 $\degree$

then it is a right angle

it is a right angle

Identify the conclusion:

If an angle measures 90 $\degree$ , then it is a right angle.

if an angle measures 90 $\degree$

an angle measures 90 $\degree$

then it is a right angle

it is a right angle

Identify the converse:

If an angle measures 90 $\degree$ , then it is a right angle.

If an angle measures 90 $\degree$ , then it is a right angle.

If an angle is a right angle, then it measures 90 $\degree$ .

If an angle does not measure 90 $\degree$ , then it is not a right angle.

Determine the biconditional statement for the following:

If an angle measures 90 $\degree$ , then it is a right angle.
If an angle is a right angle, then it measures 90 $\degree$ .

An angle is a right angle if and only if it measures 90 $\degree$ .

When an angle measures 90 $\degree$ , then it is a right angle.

An angle cannot be a right angle unless it measures 90 $\degree$ .

A biconditional statement..

is an "if/then" statement

uses the phrase "if and only if"

is the first part of a statement

is the second part of a statement

Write a definition of congruent angles as a biconditional statement.

Angles are congruent if they have the same size and shape.

If angles are congruent, then they have the same size and shape.

Congruent angles are the same.

Angles are congruent if and only if they have the same size and shape.

Write a definition of a right angle as a biconditional statement.

An angle is a right angle if and only if it has a measure of 90 degrees.

An angle has a measure of 90 degrees if and only if it is a right angle.

Right angles are 90 degrees.

If an angle is a right angle, then it has a measure of 90 degrees.

Select the conditional statement(s) of the biconditional statement.

Points are collinear if and only if they all lie in one line.

If collinear points lie in one line, then they are a line.

If points all lie in one line, then they are collinear.

Collinear points lie in one line.

If points are collinear, then they all lie in one line.

Select the conditional statement(s) of the biconditional statement:

Points lie in one plane if and only if they are coplanar.

Coplanar points lie in one plane.

If points lie in one plane, then they are coplanar.

If points are coplanar, then they lie in one plane.

Planes have coplanar points.

10.

Identify the hypothesis and conclusion:

If $3x-7=32$ , then $x=13.$

Hypothesis: $3x-7=32$
Conclusion: $x=13$

Hypothesis: $x=13$
Conclusion: $3x-7=32$

11.

Match the following

$\sim p$

Negation of the hypothesis

$\sim q$

Negation of the conclusion

$p$

Hypothesis

$q$

Conclusion

12.

A statement that contains the phrase “if and only if”

converse

inverse

biconditional

contrapositive

13.

Which type of statement is:

Two lines are perpendicular if and only if they intersect and 90 degrees.

Biconditional

Converse

Contrapositive

Inverse

14.

Which of the following statements are Conditional Statements

I am not sure if that is an acute angle

If an angle is a straight angle, then it measures 180°

I do not like cauliflower.

If you play basketball, then you know how to dribble.

15.

What is this mean?

Conditional Statement

Converse

Inverse

Contrapositive

16.

What does this mean?

Conditional Statement

Inverse Statement

Converse Statement

Contrapositive Statement

17.

What is this?

Conditional Statement

Inverse

Converse

THIS IS A GEOMETRY CLASS!!! GIVE ME NUMBERS!

18.

When writing a biconditional statement, we use the phrase ___ between the hypothesis and conclusion.

then

if and only if

always

19.

Rewrite the following statement as a biconditional: "Supplementary angles add up to 180"

If two angles add up to 180^o then they are supplementary.

You can't it is conditional.

Two angles are supplementary if and only if the sum of the measure of the two angles is 180^o.

If two angles sum does not equal 180^othen they are notsupplementary.

20.

Select the if-then statements that could have formed the following biconditional.

Two lines are perpendicular if and only if their slopes are opposite reciprocals.

If two lines are perpendicular, then their slopes are the same.

If two lines are perpendicular, then their slopes are opposite reciprocals.

If two lines have opposite reciprocal slopes, then they are perpendicular.

If two lines have opposite reciprocal slopes, then they are parallel.

Two lines will always be parallel or perpendicular.

21.

What has to happen in order to write a biconditional statement?

The conditional has to be true

The converse of the conditional has to be true

BOTH must be true.

NEITHER must be true.

22.

Which of the following is a biconditional statement?

If you do not vote, then you are not at least 18 years old.

You can vote, if and only if, you are 18 years old.

If you are 18 years old, then you can vote.

23.

In order for a statement to be biconditional, both the conditional and converse statements need to be ____.

true

false

24.

Points A, B, and C, are collinear

True

False

25.

Angle DCB and Angle DCH are supplementary

True

False

26.

Line DH is perpendicular to Line EH

True

False

27.

Line HE is perpendicular to Line AF

True

False

28.

Angles DCB and ABC are complementary.

True

False

29.

Line BH bisects angle DCG

True

False

30.

Which is a counterexample to the following statement?

If two angles are supplementary, then they are both $90\degree$ .

$45\degree$ and $45\degree$

$100\degree$ and $80\degree$

$120\degree$ and $10\degree$

$22\degree$ and $68\degree$

31.

If it is an angle, then it is acute. What is an appropriate counterexample?

70⁰

45⁰

120⁰

True. There is no counterexample.

32.

If it is a number, then it is either positive or negative. What is an appropriate counterexample?

-2

True. There is no counterexample.

33.

Organize these options into the right categories

Categorize the following

Prime Numbers (4)

Composite Numbers (4)

Special Numbers (2)

34.

Which is the definition of an even number?

A number that can not be divided by 2

A number that ends in 2, 4, 6, 8

A number that is evenly divisible by 2

A number that when split into two equal groups will have one remaining

35.

Which is the definition of an odd number?

A number that is divisible by 2

A number that ends in 3, 5, 7, 9

A number that ends in 2, 4, 6, 8

A number that when split into two equal groups will have one remaining

36.

Composite numbers:

Are always bigger than prime numbers

Have more than 2 factors

Have 2 pairs of factors

Don't have factors

37.

What are all prime numbers divisible by?

1, 2, and itself

1 and itself

Every number from 1-10

They aren't divisable at all

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Q1,HW #23 - Biconditional Statements

Total questions: 37

Worksheet time: 3hrs 31mins

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