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Math: Proving Statements - Tutorial
We will cover:
- axioms, theorems. properties, and rules
- proving statements
Proving statements in algebra and geometry makes it possible to:
- analyze each part of the equation you are solving
- develop a logical order for how equations are solved
- prove whether or not the statement is true or only assumed to be true
For a list of axioms, theorems, properties, and rules, click here.
Axioms, Theorems, Properties, and Rules
Proving Statements
The first step is recognizing the statement that needs to be proved. It is identified
as the part that says "Prove". The Statements and Reasons that follow are called "Proof".
When a statement is a condition and starts with the word "if" followed by the word
"then", use the if part first in your Statements column, if no other statement has been already provided. Then, place the word "Given" beside it in the Reason column because it is the part that has already been provided or "given".
Your goal is to come to the "then" part of the statement by the time you reach the end of your solving process. This means that you will write the "then" part as the
last statement in your Statements column, followed by the reason that supports that statement.
Once you have provided the reason for the "then" part, you have successfully proved your statement.
The statements have to progress logically until the final reason has been given. Creating a table is optional and helps to keep the statements separate from their reasons.
Now let's suppose the statement does not contain an "if, then" statement, and the statements have already been provided. For practice, the reasons used to prove each statement have also been provided. See the Explanation of Reasons below for additional help.
