Download Proving Theorems about Lines and Angles

Name _______________________________________ Date ___________________ Class __________________
Choose the best answer.
Refer to the figure for Exercises 5–6.
1.Consider the related biconditional statement
for the conditional statement “If Shelly
lives in Texas, then she lives in the
United States.”
Which of the following statements is true
about the related biconditional
statement?
A The biconditional is true because the
conditional is true.
B The biconditional is false because
the conditional and its converse are
false.
C The biconditional is true because the
conditional and its converse are true.
D The biconditional is false because
the converse of the conditional is
false.
5. Which pair of angles are corresponding
angles?
F 1 and 4
H 2 and 5
G 6 and 8
J 8 and 7
6. Which pair of angles are alternate
exterior angles?
A 4 and 8
C 3 and 7
B 2 and 5
D 1 and 4
7.What is the value of x?
x 1
 8, what justifies
2
x  1  16?
2. If
A Subtraction Property of Equality
B Division Property of Equality
C Transitive Property of Equality
8.Which could you use to show that u || v?
D Multiplication Property of Equality
3.If 5  2k, what justifies 2k  5?
F Multiplication Property of Equality
G Division Property of Equality
H Symmetric Property of Equality
J Reflexive Property of Equality
4. Which completes the statement?
If RS  GH, then ______ by the
Symmetric Property of Congruence.
F RS  GH
H GH  RS
G RS  RS
J RS  GH
A 1 and 8 are supplementary.
B 4 and 8 are supplementary.
C 3 and 7 are congruent.
D 7 and 8 are congruent.
9.Show that the conjecture is false by finding
a counterexample. When the letters i and
e appear next to each other in a word, the
letter i always comes before the letter e.
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10. Why is m  n?
F If two coplanar lines are
perpendicular to the same line, then
the two lines are parallel to each
other.
14.How many angles are formed by two lines
and a transversal?
________________________________________
15. What is the name given to the angle pair
3 and 5?
G If two parallel lines are cut by a
transversal, then the pairs of sameside interior angles are
supplementary.
H In a plane, if a transversal is
perpendicular to one of two parallel
lines, then it is perpendicular to the
other line.
J If two intersecting lines form a linear
pair of congruent angles, then the
lines are perpendicular.
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16. If parallel lines are intersected by a
transversal, how many pairs of
corresponding angles are there?
________________________________________
11.If 2  8, then r  s by which theorem?
18.What is the length of the longest side
of the triangle?
________________________________________
12.If two coplanar lines are cut by a
transversal so that right angles are
formed, how many different angle
measures are there?
F 8.5
H 40
G 26
19. What is mW ?
________________________________________
13.If parallel lines are intersected by a
transversal, how many pairs of
corresponding angles are there?
A 35
C 81
B 40.3
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20.What is the value of x if the acute angles
of a right triangle measure 8x and 12x?
Refer to the figure for Exercises 26 and 27.
21. In the figure, PQR  UVW. What is
mR?
26. What is MP?
A 1
C 4
B 2
D 5
27.What is LP?
22. If ABC  KJC, which statement is NOT
necessarily true?
F 7.5
H 2.5
G 2.5
J 7.5
28. GJ bisects FGH, mFGJ  (7x  9)°,
and mHGJ  (2x  36)°. What is
mFGH?
A ACB  KCJ
C JK  BC
B J  B
23. Suppose S  N, J  I,
A  T, JS  IN, JA  IT , and
AS  TN. Which is true?
F JSA  ITN
G JSA  NTI
H JSA  INT
Refer to the figure for Exercises 24 and 25.
24. Which represents the name of the ray
whose endpoint is K and that passes
through R?
A RK
C KS
B KT
D RK
25. In the diagram, how many different rays
have endpoint R?
F 1
H 3
G 2
J 4
F 43°
H 86°
G 54°
J 108°
29. Identify the hypothesis of the conditional
statement “Two angles are
complementary if the sum of their
measures is 90 degrees.”
F if
G Two angles are complementary
H the sum of their measures is
90 degrees
J Two angles are complementary if the
sum of their measures is 90 degrees.
30. Which conditional statement has the
same truth value as this statement?
“The sum of two odd numbers is even.”
A If two even numbers are added, then
their sum is even.
B If an even and odd number are
added, then their sum is even.
C If two even numbers are multiplied,
then their product is odd.
D If two odd numbers are multiplied,
then their product is even.