Final Exam Review – Chapters 1-4 Name _________________________

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Final Exam Review – Chapters 1-4 Name _________________________

CHAPTER 1

Can you make each conclusion from the information in the diagram? Explain.

1.

2.

3.

4.

and

and

5. Algebra a.

x

b.

MR

c.

RP

are supplementary

are complementary

Use the figure to find each of the following.

Use the figure to find each measure in Exercises 6–11.

6.

7.

9.

10.

8.

11.

Find the distance between each set of points to the nearest tenth AND the midpoint.

12.

M

(3, 2),

N

(7, 9)

13.

,

D

(5, 5)

14.

R

(0, 12),

CHAPTER 2

For each statement, (a) write the converse, and (b) decide whether the converse is true or false.

1.

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

2.

If George lives in Texas, then he lives in the United States.

3.

If two angles are vertical angles, then they are congruent.

For Exercises 4–8, name the property that justifies each statement.

4.

If and , then

.

5.

If and , then .

6.

If

7.

If

8.

, then

, then .

.

9. Use the diagram at the right to find the measure of each angle. a.

b.

c.

e.

d.

f.

For Exercises 10–11, find the value of the variable in each diagram.

10. 11.

For Exercises 12–13, use deductive reasoning to draw any possible conclusions. Write not

possible

if you cannot draw any conclusions.

12.

If Susan gets a hit this inning, then we will win. Susan hits a triple.

13.

If two angles are complementary, then the sum of their measures is 90. plementary.

14. Rewrite the following biconditional as two conditionals:

A quadrilateral is a rectangle if and only if it has four right angles.

and are com-

15.

Give a reason for each step.

Given

a.

___________________________

b.

___________________________

c.

___________________________

CHAPTER 3

Find

1.

and . State the theorems or postulates that justify your answers.

2. 3.

4. 5. 6.

Find the values of the variables.

7. 8.

9.

What is the interior angle sum of a convex 35-gon?

10.

What is the measure of an exterior angle of a regular 20-gon?

CHAPTER 4

Find the values of the variables.

1. 2.

State the postulate or theorem you would use to prove each pair of triangles congruent. If the triangles cannot be proved congruent, write not possible.

3. 4. 5.

6. 7. 8.

9.

Complete the following two-column proof by providing the best possible reasons.

Given:

Prove:

Statements

1.

2.

3.

4.

5.

6.

Reasons a.

_______________________

b.

_______________________

c.

_______________________

d.

_______________________

e.

_______________________

f.

_______________________

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