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# Chapter 7

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by

## Josh Truax

on 21 June 2017

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#### Transcript of Chapter 7

7.1 - Parallel Lines and Related Angles
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
Full transcript