ANSWER: Sample answer: Yes; since the alternate exterior
angles are congruent, the backrest and footrest are
parallel.
3-5 Proving Lines Parallel
Given the following information, determine
which lines, if any, are parallel. State the
postulate or theorem that justifies your answer.
Given the following information, determine
which lines, if any, are parallel. State the
postulate or theorem that justifies your answer.
1. ANSWER: j || k; converse of corresponding angles postulate
9. ANSWER: u || v; Alternate Exterior Angles Converse
3. ANSWER: alternate exterior angles converse
11. ANSWER: r || s; Consecutive Interior Angles Converse
5. SHORT RESPONSE Find x so that m || n. Show
your work.
13. ANSWER: u || v; Alternate Interior Angles Converse
15. ANSWER: r || s; Corresponding Angles Converse
ANSWER: 20
Find x so that m || n. Identify the postulate or
theorem you used.
7. RECREATION Is it possible to prove that the
backrest and footrest of the lounging beach chair are
parallel? If so, explain how. If not, explain why not.
17. ANSWER: 22; Conv. Corr.
s Post.
ANSWER: 43; Consec. Int.
s Conv.
ANSWER: Sample answer: Yes; since the alternate exterior
angles are congruent, the backrest and footrest are
parallel.
Given the following information, determine
which lines, if any, are parallel. State the
postulate or theorem that justifies your answer.
eSolutions Manual - Powered by Cognero
19. Page 1
r || s; Sample answer: The corresponding angles are
congruent.
Since the measures of angles are equal, the lines are
parallel.
17. ANSWER: 3-5 Proving
22; Conv.Lines
Corr.Parallel
s Post.
37. ERROR ANALYSIS Sumi and Daniela are
determining which lines are parallel in the figure at
the right. Sumi says that since 1 2, Daniela disagrees and says that since 1 2,
correct? Explain.
19. ANSWER: 43; Consec. Int.
Is either of them s Conv.
ANSWER: Daniela; 1 and 2 are alternate interior angles for
and
, so if alternate interior angles are
congruent, then the lines are parallel.
21. 44. Which of the following facts would be sufficient to
prove that line d is parallel to
ANSWER: 36; Alt. Ext. s Conv.
Determine whether lines r and s are parallel.
Justify your answer.
A
B
C
D
33. ANSWER: r || s; Sample answer: The corresponding angles are
congruent.
Since the measures of angles are equal, the lines are
parallel.
37. ERROR ANALYSIS Sumi and Daniela are
determining which lines are parallel in the figure at
the right. Sumi says that since 1 2, Daniela disagrees and says that since 1 2,
correct? Explain.
Is either of them ANSWER: B
2
ANSWER: H
57. Find x and y so that
ANSWER: Daniela; 1 and 2 are alternate interior angles for
and
, so if alternate interior angles are
congruent, then the lines are parallel.
eSolutions Manual - Powered by Cognero
44. Which of the following facts would be sufficient to
prove that line d is parallel to
2
47. SAT/ACT If x = 25 and y = 9, what is the greatest
2
possible value of (x – y) ?
F 4
G 58
H 64
J 70
and are perpendicular.
ANSWER: 10, 8.3
Page 2
3-5 Proving
Lines Parallel
ANSWER: 10, 8.3
eSolutions Manual - Powered by Cognero
Page 3