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Name _______________________________________ Date __________________ Class __________________
Problem Solving
Angles Formed by Parallel Lines and Transversals
Find each value. Name the postulate or theorem that you used to find the values.
1. In the diagram of movie theater seats,
the incline of the floor, f, is parallel to
the seats, s.
2. In the diagram, roads a and b are parallel.
If m168, what is x?
________________________________________
What is the measure of PQR?
________________________________________
3. In the diagram of the gate, the horizontal bars
are parallel and the vertical bars are parallel.
Find x and y.
________________________________________
________________________________________
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Use the diagram of a staircase railing for Exercises 4 and 5. AG || CJ and AD || FJ .
Choose the best answer.
4. Which is a true statement about the measure of DCJ?
A It equals 30, by the Alternate Interior Angles Theorem.
B It equals 30, by the Corresponding Angles Postulate.
C It equals 50, by the Alternate Interior Angles Theorem.
D It equals 50, by the Corresponding Angles Postulate.
5. Which is a true statement about the value of n?
F It equals 25, by the Alternate Interior Angles Theorem.
G It equals 25, by the Same-Side Interior Angles Theorem.
H It equals 35, by the Alternate Interior Angles Theorem.
J It equals 35, by the Same-Side Interior Angles Theorem.
© Houghton Mifflin Harcourt Publishing Company
Holt McDougal Analytic Geometry
Name _______________________________________ Date __________________ Class __________________
Problem Solving
1. 17; Alt. Int. s Thm.
2. 102; Alt. Ext. s Thm.
3. x  10; y  3; (12x  2y)°  126° by the
Corr. s Post. and (3x  2y)°  36° by the
Alt. Int. s Thm.
4.
D
5. H
Reading Strategies
1. 1  5
2. 2  6
3. 3  7
4. 4  8
5. 2  8
6. 3  5
7. 1  7
8. 4  6
9. m2  m5  180°
10. m3  m8  180°
11. m6  47° by the Corresponding
Angles Postulate
12. m3  133° by the Same-Side Interior
Angles Theorem
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
1. x  11; y  5; m1  57°; m2  57°;
m3  123°
PROVING LINES PARALLEL
Practice A
1. parallel
2.
2. Conv. of Corr. s Post.
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.
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.
Practice B
1. m  n; Conv. of Alt. Int. s Thm.
2. m  n; Conv. of Corr. s Post.
© Houghton Mifflin Harcourt Publishing Company
Holt McDougal Analytic Geometry