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Geometry: Chapter 3Ch. 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 m135o 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=x165=xImage 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.
