​What is a Proof?

​A proof is made up of given statements that prove a mathematical concept is true.

​

In order for a proof to be proven true, it has to include multiple steps. These steps are made up of statements and reasons.

Let's try a few proofs...​

​

​Example #1: 

​Example #1: 

​Step 1:

​Mark the given information

​Example #1: 

​Step 1:

​Mark the given information

​Example #1: 

​Step 2:

​Mark the reflexive sides or vertical angles

​Example #1: 

​Step 2:

​Mark the reflexive sides or vertical angles

​Example #1: 

​Step 3:

​Choose the correct triangle congruence shortcut

​Example #1: 

​Step 3:

​Choose the correct triangle congruence shortcut

​Example #1: 

​Step 4:

​List the parts in order according to the congruence statement

​Example #1: 

​Step 4:

​List the parts in order according to the congruence statement

​Example #1: 

​Step 5:

​List the reasons for each statement.

​Example #1: 

​Step 5:

​List the reasons for each statement.

Is there more?

​Example #1: 

​Let's Review the "Algebra Properties"

​Example 2:

​1) Mark the given information

​2) Mark the reflexive sides/vertical angles

​3) Choose a shortcut

​4) List the parts in order

​5) List the reasons

​Example 3:

​1) Mark the given information

​2) Mark the reflexive sides/vertical angles

​3) Choose a shortcut

​4) List the parts in order

​5) List the reasons

​CPCTC

​CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent"

​

​This is a common reason used in a Proof.

​

​It usually comes after one of the Triangle Congruence Shortcuts.

​

​Once a pair of triangles have been proven congruent by SSS, SAS, ASA, AAS, or HL, the additional parts are also congruent by CPCTC!

​Example:

​What is reason #5?

Let's Practice...​

​