This is a series of free, online High School Geometry Video Lessons and solutions.

Videos, worksheets, solutions, and activities to help Geometry students.

### Three Undefined Terms: Point, Line, and Plane

In Geometry, we have several undefined terms: point, line and plane. From these three undefined terms, all other terms in Geometry can be defined. In Geometry, we define a point as a location and no size. A line is defined as something that extends infinitely in either direction but has no width and is one dimensional while a plane extends infinitely in two dimensions.

**Explains and demonstrates the fundamental concepts (undefined terms) of geometry: point, line, plane**

**Basic geometry concepts**

A visual 3-Dimensional Demonstration of points, lines, and planes

### Counterexample

Throughout Geometry, students write definitions and test conjectures using counterexamples. When writing definitions, counterexamples are useful because they ensure a complete and unique description of a term. If a counterexample does not exist for a conjecture (an if - then statement), then the conjecture is true.

This is a demonstration of the counterexample method.

**How to use a counterexample to prove a definition or conjecture incorrect.**

A counterexample is a way to prove a statement as being false.

This video gives 4 example problems explaining counterexamples to conditional statements.

The first 2 examples are the basics behind counterexamples.

The last 2 examples are problems you'd probably see on a quiz or test.

Examples:

1. Find the counterexample to the following conditional statement.

"If you are a high school student, then you walk to school"

2. Find the counterexample to the following conditional statement.

"If you have a dog, then its name is Spot"

3. What is a counterexample to the following statement?

"All angles are equal to or more than 90 degrees?"

a) Obtuse angles

b) Acute angles

c) Straight angles

d) Right angles

4. What is a counterexample to the following statement?

"All quadrilaterals have parallel sides?"

a) Rhombus

b) Square

c) Kite

d) Trapezoid

### Good Geometry Definition

Writing a definition is a common exercise during the early stages of Geometry.

An excellent geometry definition will classify, quantify, and not have a counterexample.

Once a term is defined, it can be used in subsequent definitions; for example, once parallel lines are defined, they can be used in the definition of a parallelogram.

**How to write a good definition that does not have a counterexample?**

### Postulate, Axiom, Conjecture

Three words that are used seemingly interchangeably in Geometry are postulate, axiom, and conjecture.

It is important, however, to know how each word is different and to know the subtle implications of using each word.

These terms are especially important when working with Geometry proofs.

**How to differentiate between the words postulate, axiom, and conjecture?**

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

Videos, worksheets, solutions, and activities to help Geometry students.

In these lessons, we will learn

- point, line and plane
- counterexample
- what is a good geometry definition
- postulate, axiom and conjecture

A visual 3-Dimensional Demonstration of points, lines, and planes

This is a demonstration of the counterexample method.

A counterexample is a way to prove a statement as being false.

This video gives 4 example problems explaining counterexamples to conditional statements.

The first 2 examples are the basics behind counterexamples.

The last 2 examples are problems you'd probably see on a quiz or test.

Examples:

1. Find the counterexample to the following conditional statement.

"If you are a high school student, then you walk to school"

2. Find the counterexample to the following conditional statement.

"If you have a dog, then its name is Spot"

3. What is a counterexample to the following statement?

"All angles are equal to or more than 90 degrees?"

a) Obtuse angles

b) Acute angles

c) Straight angles

d) Right angles

4. What is a counterexample to the following statement?

"All quadrilaterals have parallel sides?"

a) Rhombus

b) Square

c) Kite

d) Trapezoid

Writing a definition is a common exercise during the early stages of Geometry.

An excellent geometry definition will classify, quantify, and not have a counterexample.

Once a term is defined, it can be used in subsequent definitions; for example, once parallel lines are defined, they can be used in the definition of a parallelogram.

It is important, however, to know how each word is different and to know the subtle implications of using each word.

These terms are especially important when working with Geometry proofs.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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