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Name _______________________________________ Date __________________ Class __________________
LESSON
3-3
Practice A
Proving Lines Parallel
1. The Converse of the Corresponding Angles Postulate states that if two coplanar
lines are cut by a transversal so that a pair of corresponding angles is congruent,
then the two lines are ____________________.
Use the figure for Exercises 2 and 3. Given
the information in each exercise, state the
reason why lines b and c are parallel.
2. 4  8
3. m3  68, m7  (5x + 3), x  13
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_________________________________________
________________________________________
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Fill in the blanks to complete these theorems about parallel lines.
4. If two coplanar lines are cut by a ______________________ so that a pair of
alternate interior angles are ______________________, then the two lines are
parallel.
5. If two coplanar lines are cut by a transversal so that a pair of same-side interior
angles are ______________________, then the two lines are parallel.
6. If two coplanar lines are cut by a transversal so that a pair of alternate exterior
angles are congruent, then the two lines are ______________________.
7. Shu believes that a theorem is missing from the lesson. His conjecture is that if
two coplanar lines are cut by a transversal so that a pair of same-side exterior
angles are supplementary, then the two lines are parallel. Complete the
two-column proof with the statements and reasons provided.
Given: 1 and 3 are supplementary.
Prove: m || n
Proof:
Statements
m || n
2 and 3 are supplementary.
Given
 Supps. Thm.
Reasons
1. 1 and 3 are supplementary.
1. a. ___________________________
2. b. ___________________________
2. Linear Pair Thm.
3. 1  2
3. c. ___________________________
4. d. ___________________________
4. Conv. of Corr. s Post.
Name _______________________________________ Date __________________ Class __________________
LESSON
3-3
Practice B
Proving Lines Parallel
Use the figure for Exercises 1–8. Tell whether lines m and n
must be parallel from the given information. If they are, state
your reasoning. (Hint: The angle measures may change for
each exercise, and the figure is for reference only.)
1. 7  3
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3. 7  6
2. m3  (15x  22)°, m1  (19x  10),
x8
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4. m2  (5x  3)°, m3  (8x  5),
x  14
________________________________________
__________________________________________
________________________________________
__________________________________________
5. m8  (6x  1)°, m4  (5x  3)°, x  9
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7. 1  5
________________________________________
6. 5  7
__________________________________________
8. m6  (x  10)°, m2  (x  15)
__________________________________________
9. Look at some of the printed letters in a textbook. The small horizontal and
vertical segments attached to the ends of the letters are called serifs. Most of the
letters in a textbook are in a serif typeface. The letters on this page do not have
serifs, so these letters are in a sans-serif typeface. (Sans means “without” in French.)
The figure shows a capital letter A with serifs. Use the given information to write a
paragraph proof that the serif, segment HI, is parallel to segment JK .
Given: 1 and 3 are supplementary.
Prove: HI || JK
Name _______________________________________ Date __________________ Class __________________
LESSON
3-3
Practice C
Proving Lines Parallel
1. p || q, m1  (6x  y  4), m2 
(x  9y  1), m3  (11x  2)
Find x, y, and the measures of
1, 2, and 3.
________________________________________________________________________________________
2. Use the figure and the given information to write a paragraph proof
that the sum of the measures of the three angles in a triangle is 180.
(Hint: Begin by constructing FG through point C and parallel to AB. )
Given: ABC is a triangle.
Prove: m1  m2  m3  180
3. In an isosceles triangle, at least two of the angles are congruent. To construct
isosceles triangle DEH, begin by drawing DE and DF . If you copy FDE and let
the angle open in the same direction, the ray would be parallel to DF . Instead,
copy FDE and draw EG so that the ray intersects DF . Label the intersection
point H. Use your compass to measure DH and EH. What is remarkable about
the measures of these segments?
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4. Construct another isosceles triangle with angles and side lengths different from
the triangle you drew in Exercise 3. Again measure the lengths of the sides
opposite the congruent angles. Write a conjecture about the measures of the
side lengths in isosceles triangles.
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___________________________________________________
___________________________________________________
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1. x  11; y  5; m1  57°; m2  57°;
m3  123°
LESSON 3-3
Practice A
1. parallel
2. Conv. of Corr. s Post.
2.
3. m7 = 68°, 3  7, Conv. of Corr. s
Post.
4. transversal; congruent
5. supplementary
6. parallel
7.
Statements
1. 1 and 3 are
supplementary.
Reasons
1. a. Given
2. b. 2 and 3 are
supplementary.
2. Linear Pair Thm.
3. 1  2
3. c.  Supps. Thm.
4. d. m  n
4. Conv. of Corr. s
Post.
Practice B
1. m  n; Conv. of Alt. Int. s Thm.
2. m  n; Conv. of Corr. s Post.
3. m and n are parallel if and only if
m7  90°.
4. m  n; Conv. of Same-Side Int. s Thm.
5. m and n are not parallel.
6. m  n; Conv. of Corr. s Post.
7. m  n; Conv. of Alt. Ext. s Thm.
8. m and n are not parallel.
9. Sample answer: The given information
states that 1 and 3 are
supplementary. 1 and 2 are also
supplementary by the Linear Pair
Theorem. Therefore 3 and 2 must
be congruent by the Congruent
Supplements Theorem. Since 3 and
2 are congruent, HI and JK are
parallel by the Converse of the
Corresponding Angles Postulate.
Practice C
Possible answer: Construct FG
through point C and parallel to AB . 3
and 4 are a linear pair, so m3 
m4  180° by the Linear Pair
Theorem. But the Angle Addition
Postulate shows that m4  mACF 
mFCD, so by substitution m3 
mACF  mFCD  180°. m1 
mACF by the Alternate Interior Angles
Theorem and m2  mFCD by the
Corresponding Angles Postulate.
Therefore m1  m2  m3  180°
by substitution.
3. The measures of the segments are
equal.
4. Possible answer: If a triangle is
isosceles, then the sides opposite the
congruent angles are congruent.