Geometry: Section 3.3

Properties of Parallel Lines

Two lines are parallel iff they are coplanar and do not intersect.

To indicate that is parallel to we write _______

Arrowheads are use toindicate parallel lines in a figure.

AB CDCDAB //

Noncoplanar lines which do not intersect are called skew.

Recall that perpendicular lines are

angles.right form tointersect that lines two

Postulate 13: The Parallel Postulate

If there is a line and a point not on the line, then there is exactly one line through the point

that will be parallel to the given line.

Postulate 14: The Perpendicular Postulate

If there is a line and a point not on the line, then

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Postulate 15Corresponding Angles Postulate

(CAP)

If two parallel lines are cut by a transversal, then corresponding

angles are congruent.

Theorem 3.4Alternate Interior Angles Theorem

(AIAT)

If two parallel lines are cut by a transversal, then alternate interior

angles are congruent.

Theorem 3.5Same-Side Interior Angles Theorem

(SSIAT)

If two parallel lines are cut by a transversal, then same-side interior

angles are supplementary.

Theorem 3.6Alternate Exterior Angles Theorem

(AEAT)

If two parallel lines are cut by a transversal, then alternate exterior

angles are congruent.

Examples: Find the value of the variable in each problem.

xxxx

4416

11753

Examples: Find the value of the variable in each problem.

6.1818610

18061018011753

yyy

yy

Examples: Find the value of the variable in each problem.

75.201668

1801481806385

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ww

Theorem 3.7 Perpendicular Transversal Theorem

If a transversal is perpendicular to one of two parallel lines, then

line. parallel second thelar toperpendicu also is al transversthe