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Unit 1: Parallel and Perpendicular Lines and Planes (including Coordinate geometry)

Lesson 7: Proving Lines Parallel (3-5)

Objectives:
• Recognize angle pairs that occur with parallel lines
• Prove that two lines are parallel

In the previous lesson of this unit we learned that if parallel lines are intersected by a transversal,
then corresponding angles are congruent
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1
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In a similar manner we can use any of the parallel line theorems (but ‘in reverse’) to prove that a pair
of lines is parallel:
Corresponding Angles bi-conditional (Postulates 3
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4): Two lines cut by a transversal are
parallel if and only if corresponding angles are congruent
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1/3
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Consecutive Interior Angles (CIA) bi-conditional (Theorems 3
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6): Two lines cut by a
transversal are parallel if and only if consecutive interior angles are supplementary
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3/3
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Example 1 – Use the diagram and the given information to determine if line j is parallel to line k
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Once
proved true, a theorem can then be used in the proof of other theorems
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The postulates below are
also relevant to the constructions for this unit
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!∠1 ≅ ∠2,∠4 ≅ ∠5

2
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 

Q
3
2 T

P

4

R

5

1

6

S

REASONS
1
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3
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Vertical angles
Transitive


4
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210 #1-5

PPS p
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211-2 #9-21
odd; 25-28; 33-35

Level 3 -
Extension
HOT p

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