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Guidance

A
two column proof
is one common way to organize a proof in geometry. Two column proofs always have two columns- statements and reasons. The best way to understand two column proofs is to read through examples.

When writing your own two column proof, these keep things in mind:

Number each step.

Start with the given information.

Statements with the same reason can be combined into one step
. It is up to you.

Draw a picture and mark it with the given information.

You must have a reason for EVERY statement.

The order of the statements in the proof is not always fixed, but make sure the order makes logical sense.

Reasons will be definitions, postulates, properties and previously proven theorems.
“Given” is only used as a reason if the information in the statement column was told in the problem.

Use symbols and abbreviations for words within proofs.
For example,
can be used in place of the word
congruent
. You could also use
for the word angle.

Example A

Write a two-column proof for the following:

If
, and
are points on a line, in the given order, and
, then
.

When the statement is given in this way, the “if” part is the given and the “then” part is what we are trying to prove.