Transversal ->

a line that intersects two coplanar lines at two distinct points.

Alternate Interior Angles ->

angles on opposite sides of the transversal within the parallel lines

Same-side Interior Angles ->

angles on the same side of the transversal within the parallel lines

Corresponding Angles ->

angles on the same side of the transversal, one inside and one outside but not adjacent to one another

Postulates and Theorems

Postulate 7.1 - Corresponding Angles Postulate

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

Theorem 7.1 - Alternate Interior Angles Theorem

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

Theorem 7.2 - Same-Side Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of same-side interior angles are supplementary.

7.2 - Proving Lines Parallel

Postulate 7.2 - Converse of Corresponding Angles Postulate

It two lines are cut by a transversal so that a pair of corresponding angles are congruent, then the lines are parallel.

Theorem 7.3 - Converse of Alternate Interior Angles Theorem

If two lines are cut by a transversal so that a pair of alternate interior angles are congruent, then the lines are parallel.

Theorem 7.4 - Converse of Same-Side Interior Angles Theorem

If two lines are cut by a transversal so that a pair of same-side interior angles are supplementary, then the lines are parallel.

7.3 - Parallel Lines and Exterior Angles

Alternate Exterior Angles ->

angles on opposite sides of the transversal and both located outside the parallel lines

Same-Side Exterior Angles ->

angles on the same side of the transversal and both located outside the parallel lines

Exterior Angle Theorems

Theorem 7.5 - Alternate Exterior Angles Theorem

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

Theorem 7.6 - Same-Side Exterior Angles Theorem

If two parallel lines are cut by a transversal, then same-side exterior angles are supplementary.

Exterior Angle Converses

Theorem 7.7 - Converse of Alternate Exterior Angles Theorem

It two lines are cut by a transversal so that a pair of alternate exterior angles are congruent, then the lines are parallel.

Theorem 7.8 - Converse of Same-Side Exterior Angles Theorem

If two lines are cut by a transversal so that a pair of same-side exterior angles are supplementary, then the lines are parallel.

7.4 - Parallel Lines and Perspective Drawing

Perspective Drawing ->

a way of drawing objects on a flat surface so that they look the same as they appear to the eye.

Vanishing Point ->

a point on the "horizon" of a picture where parallel lines "meet"

One-Point Perspective ->

uses one vanishing point

Two-Point Perspective ->

uses two vanishing points

Homework #8

(Section 7.1 - 7.4)

#1 - 7 odd and #30-36 even

Page 366 - 368

#6 - 14 even and #22 - 26 even

Page 373 - 374

#1 - 9 odd

Page 388 - 389

Quiz #5

**Chapter 7**

**Reasoning and Parallel Lines**