Page 63 - Math Course 2 (Book 2)

Congruent Angels in Parallel Lines
Mo. 8

Lesson 6

KEY CONCEPTS:
1. Use the properties of parallel lines to
determine congruent angles.
2. Use algebra to find angle measures.

MO. 8 - L6a POSTULATE 3.1

Finding Measures of Corresponding Angles Postulate
Congruent Angels If two parallel lines are cut by a transversal, then
each pair of corresponding angles is congruent.
THEOREM 3.4 Example:

Perpendicular Transversal Theorem ∠1 ≅ ∠5, ∠2 ≅ ∠6, ∠3 ≅ ∠7, ∠4 ≅ ∠8,

In a plane, if a line is perpendicular to one of two
parallel lines, then it is perpendicular to the other.
l 1 2
3 4
m

5 6
n 7 8

THEOREM Parallel Lines and Angle Pairs

Theorems Examples Model

Alternate Interior Angles If two parallel lines ∠4 ≅ ∠5
3.1 are cut by a transversal, then each pair of
alternate interior angles is congruent. ∠3 ≅ ∠6

∠4 and ∠6 are 1 2
Consecutive Interior Angles If two parallel supplementary 3 4
3.2 lines are cut by a transversal, then each pair of 5 6
consecutive interior angles is supplementary. ∠3 and ∠5 are 7 8
supplementary
Alternate Exterior Angles If two parallel lines ∠1 ≅ ∠8
3.3 are cut by a transversal, then each pair of
alternate exterior angles is congruent. ∠2 ≅ ∠7

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