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**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.**

_______________________