Determining Angle Measure With Parallel Lines Worksheets With Answer Key - Johnny Wolfe, Jay High School Santa Rosa County Florida - 2001 Page 3
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138. Alternate Exterior Angle Theorem – If two lines are cut by a transversal, then
each pair of alternate exterior angles is congruent.
The proof of the Alternate Exterior Angle Theorem is given below in a
paragraph proof. The statements and reasons are written informally in a
paragraph. But the steps in a paragraph proof are the same as those in a two-
column proof.
Given: l || q and l is a transversal of p and q.
Prove: ∠ 1 ≅ ∠ 8; ∠ 2 ≅ ∠ 7
Paragraph Proof:
We are given that p || q. If two parallel lines are cut
by a transversal, corresponding angles are congruent.
So, ∠ 1 ≅ ∠ 5 and ∠ 2 ≅ ∠ 6. ∠ 5 ≅ ∠ 8 and ∠ 6 ≅ ∠ 7
because vertical angles are congruent. Therefore, ∠ 1 ≅ ∠ 8
and ∠ 2 ≅ ∠ 7 since congruence of angles is transitive.
9. Example – Find the values of x, y, and z.
Since AG || BH , ∠ CEF ≅ ∠ EFH by the alternate interior
angle theorem.
m ∠ CEF = m ∠ EFH
2x = 82
x = 41
Since CD || EF , ∠ DCE and ∠ CEF are supplementary by
the consecutive interior angle theorem.
m ∠ DCE +m ∠ CEF = 180
7z + 2x = 180
7z + 2(41) = 180
m ∠ BDI = m ∠ EFH
7z = 98
5y + 7 = 82
z = 14
5y = 75
y = 15
Since CD || EF , ∠ BDI ≅ ∠ EFH by the alternate exterior
angle theorem.
Therefore, x = 41, y = 15, and z= 14
Johnny Wolfe Determining Angle Measure with Parallel Lines
Jay High School
Santa Rosa
County Florida
September 14, 2001
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