# Two Column Proof

How to solve two column proof problems: example and its solution.

## How to write?

Two column proof is a form to prove a statement.

Start from the 'given' statement.

Then derive the 'prove' statement

using logic (known theorems, laws, etc.).

In the left column, write a statement.

And in the right column,

write the reason for the statement

in the left column.

This is an example of deductive reasoning.

## Example

Start from the 'given' statements.

m∠1 + m∠2 = 90 and m∠2 + ∠3 = 90.

So m∠1 + m∠2 = m∠2 + m∠3.

This can be either transitive property or substitution.

Transitive property:

if *a* = *b* & *c* = *b*, then *a* = *c*.

Substitution:

put m∠2 + m∠3 into **1**'s right side: 90.

To subtract m∠2 from both sides,

write m∠2 = m∠2 (reflexive property),

and do the subtraction: m∠1 = m∠3

m∠1 = m∠3

Then ∠1 ≅ ∠3.

This is using the definition of congruent angles.

You got the 'prove' statement.

So this is the end of the proof.