Determining Angle Measure With Parallel Lines Worksheets With Answer Key - Johnny Wolfe, Jay High School Santa Rosa County Florida - 2001 Page 2
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135. Notice that in Example 4 above, ∠ 4 and ∠ 5 form a pair of alternate interior
angles. This is an application of another of the special relationships between the
angles formed by two parallel lines and a transversal. These relationships are
summarized in the theorems below.
6. Alternate Interior Angle Theorem – If two parallel lines are cut by a
transversal, then each pair of alternate interior angles is congruent.
The proof of the Alternate Interior Angle Theorem is given below.
Statement
Reason
P||q and transversal l
Given
∠ 3 ≅ ∠ 2
Vertical Angle Theorem
∠ 2 ≅ ∠ 6
Corresponding Angle Theorem
∠ 3 ≅ ∠ 6
Transitive Property
7. Consecutive Interior Angle Theorem – If two parallel lines are cut by a
transversal, then each pair of consecutive interior angles is supplementary.
The proof of the Alternate Exterior Angle Theorem is given below.
Statement
Reason
P||q and transversal l
Given
∠ 1 ≅ ∠ 5
Corresponding Angle Theorem
∠ 5 ≅ ∠ 8
Vertical Angle Theorem
∠ 1 ≅ ∠ 8
Transitive Property
Johnny Wolfe Determining Angle Measure with Parallel Lines
Jay High School
Santa Rosa
County Florida
September 14, 2001
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