Learning

Lessons

1. Basics
2. Deductive Reasoning

3 - Parallel lines

4 - Congruent Triangles

5 - Quadrilaterals

6 - Inequalities

7 - Similar Polygon

8 - Rt. Triangles

9 - Circles

10 - Constructions

11 - Areas of 2D objects

12 - Areas and Volumes

13 - Coordinates

14 - Reflection/Rotation

Parallel Lines

Objective:

• To be able to distinguish between skew, parallel, and intersecting lines.

• Know property of parallel

Lesson 3-1 Parallel Lines:

Parallel lines (|| Lines): coplanar lines that do not intersect.

Skew lines: non-coplanar lines. They are neither parallel nor intersecting

Transversal: Line that intersects two or more coplanar lines in different points

Alternate Interior angles: Two nonadjacent interior angles on opposite sides of the transversal.

Angle 1 and Angle 2 are alternate interior angles.

Same-side Interior angles: Two interior angles on the same side of the transversal.

Angle 1 and Angle 2 are same-side interior angles.

Corresponding angles: Two angles in corresponding positions relative to the two lines.

Angle 1 and Angle 2 are Corresponding angles.

Properties of || Lines:

Theorem 3-1

If 2 Parallel planes are cut by a third plane, then the lines of intersection are parallel.

Line l and m are both parallel

Postulate 10

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

Angle 1 and Angle 2 are Congruent.

Theorem 3-2

if two lines are CBAT (Cut by a transversal), the alternate interior angles are congruent.

Angle 1 and Angle 2 are Congruent.

Theorem 3-3

If 2 || lines are cut by a transversal, then same-side interior angles are supplementary.

Angle 1 and Angle 2 are supplementary.

Theorem 3-4

If a transversal is perpendicular to 1 of 2 || lines, then it is perpendicular to the other side also.

Angle 1 and Angle 2 are both perpendicular

Postulate 11

If 2 Parallel planes are cut by a transversal and corresponding angles are congruent, then the lines are parallel

Theorem 3-5

If 2 lines are cut by a transversal and alternate interior angles are congruent, then the lines are parallel.

The blue lines are parallel to each other since Angle 1 and Angle 2 are congruent.

Theorem 3-6

If 2 lines are cut by a transversal and same-side interior angles are supplementary, then the lines are parallel.

The blue lines are parallel to each other since Angle 1 and Angle 2 are supplementary same side interior angles.

Theorem 3-7

Through a point outside a line, there is exactly one line parallel to the given line.

Theorem 3-8

Through a point outside a line, there is exactly one line perpendicular to the given line

Theorem 3-9

Two lines parallel to a third line are parallel to each other.

Line a, line b, and line c all are parallel to each other.