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Extra Practice
Lesson 1-4
Use the figure at the right for Exercises 1-5.
is the angle bisector of
1.
.
2. Algebra BC = 3x + 2 and CD = 5x − 10. Solve for x.
3. Algebra If AC = 5x − 16 and CF = 2x − 4, then AF =
4. mBCG = 60, mGCA =
, and mBCA =
.
.
5. mACD = 60 and mDCH = 20. Find mHCA.
6. Algebra In the figure at the right, mPQR = 4x + 7.
Find mPQS.
Lesson 1-5
Name the angle or angles in the diagram described by each of the following.
7. supplementary to NQK
8. vertical to PQM
9. congruent to NQJ
10. adjacent and congruent to JQM
11. complimentary to KQP
12. XYZ and XYW are complementary angles. mXYZ = 3x + 9 and mXYW =
5x + 9. What are mXYZ and mXYW ?
13. ABC and DEF are supplementary angles. The measure of DEF is
twenty degrees less than three times the measure of ABC. What are
mABC and mDEF?
bisects RST. mQST = 2x + 18 and mRST = 6x − 2. What is
14.
mRSQ?
Lesson 2-6
Find the value of x.
15.
16.
17.
Lesson 2-2
18. Identify the hypothesis and conclusion of this conditional statement:
If you can predict the future, then you can control the future.
If the given statement is not in if-then form, rewrite it. Write the converse, inverse,
and contrapositive of each conditional statement. Determine the truth value of
each statement.
19. If 3x − 7 = 20, then x = 9.
20. The product of two even numbers is even.
For each of the statements, write the conditional form and then the converse of the
conditional. If the converse is true, combine the statements as a biconditional.
21. The number one is the smallest positive square.
22. Rectangles have four sides.
Lesson 3-1
Use the cube to name each of the following.
23. all lines that are parallel to
24. a pair of parallel planes
25. two lines that are skew to
Identify all pairs of each type of angles in the
diagram. Name the two lines and the transversal that
form each pair.
26. corresponding angles
27. alternate interior angles
28. same-side interior angles
29. alternate exterior angles
Lesson 3-2
Find m1 and m2. State the theorems or postulates that justify your answers.
30.
33.
31.
32.
34.
35.
Find the value of each variable. Then find the measure of each labeled angle.
36.
37.
38.
Lesson 3-3
Refer to the diagram at the right. Use the given information to determine which
lines, if any, must be parallel. If any lines are parallel, use a
theorem or postulate to tell why.
39. 9  14
40. 1  9
41. 2 is supplementary to 3.
42. 7  10
43. m6 = 60, m13 = 120
44. 4  13
45. 3 is supplementary to 10.
46. 10  15
47. 1  8
Find the value of x for which a || b.
48.
49.
50.