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3.2 Properties of Parallel Lines
Objectives: TSW …• Use the properties of parallel lines cut by a
transversal to determine angles measures.• Use algebra to find angle measure.
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Postulate 3.1Corresponding Angles Postulate
p
m
n
1 23 4
5 687
1 5,
If a transversal intersects two parallel lines,
then corresponding angles are congruent.
2 6, 3 7, 4 8
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Example 1: In the figure, x ‖ y and m10 = 120. Find m14.
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Theorem 3.1:Alternate Interior Angles Theorem
If a transversal intersects two parallel lines, then alternate interior angles are congruent.
p
m
n
1 23 4
5 687
4 5,3 6
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Example 2: In the figure, x ‖ y and m12 = 38. Find m15.
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Theorem 3.2: Same-Side Interior Angles Theorem
If a transversal intersects two parallel lines,
then Same Side Interior Angles are supplementary.
p
m
n
1 23 4
5 687
m4 + m6 = 180, m3 + m5 = 180
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Example 3: In the figure, x ‖ y and m12 = 43. Find m14.
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Theorem 3.3:Alternate Exterior Angles Theorem
If a transversal intersects two parallel lines, then alternate exterior angles are congruent.
p
m
n
1 23 4
5 687
1 8,2 7
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Example 4: In the figure, x ‖ y and m11 = 51. Find m16.
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Example 5: Finding measures of Angles
What are the measures of all numbered angles. Which theorem or postulate justifies each answer?
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Example 6: What is the measure of RTV?
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Example 7:If m5 = 2x – 10, m6 = 4(y – 25), and
m7 = x + 15, find x and y.
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Example 8:In the figure, m3 = 110 and m12 = 55.
Find the measure of the other angles.
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SummaryRelationship of angle measures formed by two
parallel lines cut by a transversal.
Corresponding Angles - congruent Alternate Interior Angles - congruent Alternate Exterior Angles - congruent Same Side Interior Angles - Supplementary