GEOMETRY



GEOMETRY Name ____________________________________

Chapter 2 Review Worksheet Period ________ Date ______________________

Section 2-1

1. Determine the hypothesis and the conclusion from the given conditional statement.

a) If the doorbell rings, then my dog barks.

Hypothesis: ___________________________________________________________________

Conclusion: ___________________________________________________________________

2. Complete the table

|Conditional |Converse |Inverse |Contrapositive |

|If I am in math class, then Mr. Lemei|a) |b) |c) |

|is not my teacher. | | | |

| | | | |

| | | | |

|d) |e) |If it is not summer, then school is |f) |

| | |not in session. | |

| | | | |

| | | | |

| | | | |

| | | | |

| | | | |

Section 2-2

3. Biconditional Statements: Rewrite the biconditional statement as a conditional statement and its converse.

I attend CHS if and only if Mr. Mueller is my principal.

Conditional:

Converse:

4. Biconditional Statements: Rewrite the conditional statement and its converse as a biconditional statement.

Conditional: If I am a junior, then I’m in the class of 2013.

Converse: If I’m in the class of 2013, then I am a junior.

Biconditional:

5. FINDING COUNTEREXAMPLES Write the converse, then give a counterexample that shows the converse is false.

If x=2, then x2=4.

Converse:

Counterexample:

6. REWRITING STATEMENTS: Write the converse of the conditional statement. Determine if the converse is true or false. If the converse is true, combine it with the conditional statement to form a true biconditional statement. If the converse is false, provide a counterexample.

a) Conditional Statement: If two angles are a linear pair, then they are supplementary.

Converse:

True or False (Circle One)

True Biconditional OR Counterexample:

b) Conditional Statement: If two angles are complementary, then they have a sum of [pic].

Converse:

True or False (Circle One)

True Biconditional OR Counterexample:

Section 2-3

7. Write the symbolic statement in words using p and q given below.

p: [pic]is a right angle. q: The measure of [pic] is[pic].

|p ( q |~q ( ~p |~p |p ((q |

| | | | |

8. LOGICAL REASONING Decide whether inductive or deductive reasoning is used to reach the conclusion.

a) If a student is elected class president, then they received the most votes. Greg is class president. Therefore, Greg received the most votes.

Deductive OR Inductive (Circle One)

b) Every Wednesday morning Ms. O’Keefe has a staff meeting in the MPR. It is Wednesday morning, so Ms. O’Keefe goes to the MPR.

Deductive OR Inductive (Circle One)

9. Determine if statement (3) follows from statements (1) and (2) by the Law of Detachment, or the Law of Syllogism. If it does not follow either law, write invalid.

a) (1) If Tess is stung by a bee, then she needs to go to the hospital.

(2) Tess went to the hospital.

(3) Tess was stung by a bee.

Law of Detachment Law of Syllogism OR Invalid (Circle One)

b) (1) If an angle is obtuse, then its measure is greater than [pic] and less than [pic].

(2) [pic] is obtuse.

(3) [pic] has a measure that is greater than [pic] and less than [pic].

Law of Detachment Law of Syllogism OR Invalid (Circle One)

c) (1) If it is July, then it is summer.

(2) If it is summer, then school is not in session.

(3) If it is July, then school is not in session.

Law of Detachment Law of Syllogism OR Invalid (Circle One)

Section 2-4

10. Solve the equation and state a reason for each step.

a) Given: [pic] b) Given: [pic]

Statement Reason Statement Reason

Section 2-5

11. Set up an equation using the given information, then solve for the variable.

Given: [pic]and [pic]

[pic]

[pic]

Section 2-6

12. Using the figure below, decide if the statement is always true or sometimes false. Explain.

a) [pic]

b) [pic]

c) [pic]

13. Find the measure of each angle if [pic].

14. Solve for the variables.

a) b)

[pic] [pic]

15. Constructions:

a) Copy the segment provided:

b) Construct a line segment perpendicular to the segment provided:

-----------------------

C

A

B

D

E

F

1

2

3

4

1

2

3

4

5

6

7

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