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

Basics

Objective:

• Understand the basic meanings of the Geometry words: equidistant, points, line, plane, collinear, coplanar, intersection, and Angles.

Lesson 1 Basics:

Equidistant: Equidistant is the same distance as one line to the other. For example, Sarah’s high school is 1.5 miles from her house. Her middle school is also 1.5 miles from her house. The direct path from her house to the high school is equidistant to the direct path from her house to her middle school.

Points: Points are marked locations on a line. Points usually are represented by a dot and the name of the point is usually in CAPTIAL letters. For example, point A and point B.

Lines: Lines are paths traced by a moving point. Lines extend in two directions without ending. Even thought pictures show a line with thickness, there is no thickness.

Planes: Plans are flat platforms with no end or thickness. Much like a wall or a table top, but without the thickness and continues forever. Often name with a capital.

Collinear Points: Collinear Points are points that are all in one line.

Coplanar Points: Coplanar points are points all in the same plane.

Intersections: Intersections are where two figures meets or share a common set of points.

Postulate 1 (Ruler Postulate)

1. The points on a line can be paired with the real numbers in such a way that any two points can have coordinates 0 and 1.

2. Once a coordinate system has been chosen in this way, the distance between any two points equals the absolute value of the difference of their coordinates.

Postulate 2 (Segment Addition Potulate)

If B is between A and C, then AB+BC=AC

AB+BC=AC

Postulate 3 (Angle Addition Postulate)

If point B lies in the interior of angle AOC, then measure of angle AOB plus measure of angle BOC is equal to the measure of AOC.

m/ AOB +m/ BOC = m/ AOC

If angle AOC is a straight angle and B is any point not on AC, then

m/ AOB +m/ BOC = 180

Postulate 4

A line contains at least two points; a plane contains at least three points not all in one line; space contains at least four points not all in one plane.

Postulate 5

Through any two points there is exactly one line.

Postulate 6

Through any three points there is at least one plane, and through any three noncolinear points there is exactly one plane.

Postulate 7

If two points are in a plane, then the line that contains thepoints is in that plane.

Postulate 8

If two planes intersect, then their intersection is a line.

Theorem 1-1

If two lines intersect, then they intersect in exactly one point.

Theorem 1-2

Through a line and a point not in the line there is exactly one plane.

Theorem 1-3

If two lines intersect, then exactly one plane contains the lines.