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Geometry: Chapter 3
Ch. 3.3: Use Parallel Lines and
Transversals
Postulate 15: Corresponding Angles Postulate
If two parallel lines are cut by a transversal,
then the pairs of corresponding angles are
congruent.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 154.
Ex. 1 Identify
Congruent Angles
The measure of three
of the numbered
angles is 550.
Identify the angles.
Explain your
reasoning.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 155.
Theorem 3.4 Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then
the pairs of alternate interior angles are
congruent.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 155.
Theorem 3.5 Consecutive Interior Angles
Theorem
If two parallel lines are cut
by a transversal, then the
pairs of consecutive
interior angles are
supplementary.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 155.
Theorem 3.6 Alternate Exterior Angles Theorem
If two parallel lines are cut by a transversal, then
the pairs of alternate exterior angles are
congruent.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 155.
Theorem 3.7: Perpendicular Transversal
Theorem
If a transversal is perpendicular to one of two
parallel lines, then it is perpendicular to the
other.
If h || k, and j ┴ h, then j ┴ k.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 192.
Ex. 2 Use properties of parallel lines.
Find the value of x.
Solution: By the Corresponding Angles Postulate, the
angle with a m135o and the angle with a m(x 30)o are congruent.
Using the definition of congruent angles, the two angle
measures are equal.
135o= (x -30)o
135+30=x
165=x
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 155.
Ex. 3. Prove that if two parallel lines are cut
by a transversal, then the exterior angles on
the same side of the transversal are
supplementary.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 156.
Ex. 4
Determine which other lines, if any, must
be perpendicular. Explain your
reasoning.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 192.
Ex. 4
Determine which other lines, if any, must
be perpendicular. Explain your
reasoning.
Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 192.