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LESSON
3-3
Reading Strategies
Use a Graphic Organizer
Line a and line b are parallel. This can
be proven in four different ways.
In Exercises 1–4, use the given information
to determine the theorem or postulate that
proves m || n.
1. ∠1 ≅ ∠7
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2. m∠4 + m∠5 = 180°
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3. ∠5 ≅ ∠3
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4. ∠8 ≅ ∠4
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5. If m∠1 = 47° and m∠5 = 49°, are the lines parallel? Explain.
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6. If m∠3 = 119°, what does the measure of ∠6 need to be to prove m || n?
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Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
3-26
Holt McDougal Geometry
5.
Problem Solving
1. m∠1 = (8x − 1) = 8(4) − 1 = 31° Replace x with 4.
Statements
m∠2 = (6x + 7) = 6(4) + 7 = 31° Replace x with 4.
1. a. m ⊥ n
∠1 and ∠2 are corr. ∠s and they are
congruent, so the shelf is parallel to the
rafter by the Conv. of Corr. ∠s Post.
Reasons
1. Given
2. b. m∠1 = 90°, m∠2 = 90° 2. Def. of ⊥
2. m∠3 = (3y + 7) = 3(21) + 7 = 70° Replace y with 21.
m∠4 = (5y + 5) = 5(21) + 5 = 110° Replace y with 21.
m∠3 + m∠4 = 70° + 110° = 180°
∠3 and ∠4 are supp. ∠s , so the sign posts
are parallel by the Conv. of Same-Side Int.
∠s Thm.
3. A
4. J
5. m∠1 = 40° and m∠2 = 40°, so the sides
are || by the Conv. of the Alt. Int. ∠s Thm.
6. m∠3 = 90° and m∠4 = 90°, so the sides
are || by the Conv. of the Same-Side Int.
∠s Thm.
3. ∠1 ≅ ∠2
3. c. Def. of ≅ ∠s
4. m∠1 + m∠2 = 180°
4. Add. Prop. of =
5. d. ∠1 and ∠2 are a linear 5. Def. of linear pair
pair.
6. All the borders are straight lines, and the
Colorado–Utah border is a transversal to
the Colorado–Wyoming and the
Colorado–New Mexico borders. Because
the transversal is perpendicular to both
borders, the borders must be parallel.
Practice C
1.
Reading Strategies
1. Converse of the Alternate Exterior Angles
Theorem
2. Converse of the Same-Side Interior
Angles Theorem
3. Converse of the Alternate Interior Angles
Theorem
4. Converse of the Corresponding Angles
Postulate
5. No; ∠1 ≅/ ∠5.
6. 61°
2. Because BD must be shorter than BE ,
x < 11. Therefore BC is the shortest
segment. If x = 1, then BD would be the
second shortest segment, but if x = 3,
then AB would be the second shortest
segment. So there is not enough
information given in the figure to say
which is the second shortest segment.
3-4 PERPENDICULAR LINES
Practice A
1. perpendicular; midpoint
2. perpendicular
3. AB ; x < 23
4. FE ; x > 8
5. parallel
6. congruent
7. perpendicular
8. 6
9. 5
3. The distances are equal.
10. 7
Practice B
1. PR ; x < 3.5
2. HJ ; x > 7
4. x = 3, y =
3. AB ; x > 9
3
, z = −1
2
4. UT ; x < 17
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
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Holt McDougal Geometry