Introducing Basic Geometric Concepts: Points, Lines, Line Segments, Rays, and Planes. Segment Addition Postulate. Midpoint and Distance Formulas with an Introduction to The Pythagorean Theorem.

You have heard of points in geometry, or about line segments, or rays; but what tells apart one from the other? What is a plane? Is the plane the figure my teacher draws at the overhead projector? Or is the size of the wall? How should we work with the Segment Addition Postulate? How do I substitute the coordinates in the distance, or in the midpoint formulas? What should be done if I am given an endpoint, and the midpoint to find the other endpoint?

All these are questions you may be asking yourself. This lesson will enable you to find the answers to them in a very easy, and helpful way. You won't have a teacher rushing you, and you will find that the sequence, and color animations are great clues to follow the flow of the ideas. You will be given problems that you may solve on your own, and they will be graded instantly. You will love the lesson!

Lesson's Content

Lesson's Glossary

Angle
Geometric shape formed by two rays (initial and ending sides of the angle) that share a common endpoint called the vertex. You may name an angle using the vertex, or a point in each ray and the vertex label in the center.

Acute angle
An angle that is between 0 and 90 degrees.

Adjacent angles
If two angles have a common side, a common vertex and no common interior points then they are adjacent.

Collinear
In the same line.

Coplanar
Within the same plane.

Line
An infinite set of points that extends forever in two directions. 2 points on the line allows to uniquely define it.

Non-Collinear
Not in the same line.

Obtuse angle
An angle whose measure is greater than 90 but less than 180 degrees.

Plane
A two-dimensional group of points that goes on infinitely in all directions; made up of infinite lines

Point
Indicates a location in space and has no size. It is represented by a dot and usually labeled with uppercase letters. It is uniquely identified by a set of coordinates (x,y) in the plane, and (x,y,z) in the space.

Ray
The section of a line that has one endpoint in one side and it never ends at the other side. (flash light beam pointing to the space)

Segment
A section of a line, defined by two end points and all the points between them.

Interactive Geometric Applets: Relevant Theorems.

The Pythagorean Theorem states that the square of the hypotenuse is equal to

the sum of the squares of the two legs in a right triangle.

This applet verifies that relationship. You can see that the green and red areas of the squares in the legs of the triangle;

fit in the square of the hypotenuse.

As you change the dimensions of the triangle, by dragging any of the vertices;

the applet updates the calculations to comply with the Pythagorean Theorem.

One important postulate about planes states that two planes have as intersection a line.

This applet allows you to drag the slider to verify it.

To name a plane you need to use three non-collinear points. Should you use collinear

points to name a plane, you wouldn't be able to avoid ambiguity; since you may have

an infinite number of planes intersecting in the line. View the applet shown below

and interact dragging the slider to understand the need to use three non-collinear

points when naming a plane.

Vocabulary Puzzle Interactive

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