Math 109

Section 2.1

The Parallel Postulate

Definition: Perpendicular lines meet to form congruent adjacent angles.

Theorem 2.1.1: From a point not on a given line, there is exactly one line perpendicular to the given line.

Definition: Parallel lines are lines that do not intersect and lie in the same plane

Postulate 10: Through a point not on a line, exactly one line is parallel to the given line

Definition: A transversal is a line that intersects two or more lines at distinct points.

Special Angles

Figure 2.1

The angles that lie inside lines and are interior angles

The angles that lie outside lines and are exterior angles

Corresponding angles: Two angles that lie on the same side of the transversal where one angle is an interior angle and the other angle is an exterior angle.

Alternate interior angles are two interior angles that lie on opposite sides of the transversal.

Alternate exterior angles are two exterior angles that lie on opposite sides of the transversal.

Postulate 11: If two parallel lines are cut by transversal, then the corresponding angles are congruent.

Figure 2.2

Theorem 2.1.2: If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

In figure 2.2,

Theorem 2.1.3: If two parallel lines are cut by a transversal, then the alternate interior angles are congruent.

In figure 2.2,

Theorem 2.1.4: If two parallels lines are cut by a transversal, then the interior angles on the same side of the transversal are supplementary.

In figure 2.2,

Theorem 2.1.5: If two parallel lines are cut by a transversal, then the exterior angles on the side of the transversal are supplementary.

In figure 2.2,

Examples page 73-74

Use for examples 2 and 4

2)

4)

6) In a plane, and. By appearance how are related.

14)

16)

Multiply equation 2 by -1 and add to equation 1