Two Column Proof

Two Column Proof

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

How to write?

Start from the 'given' statement. Then derive the 'prove' statement using logic.

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

Given: the measure of angle 1 + the measure of angle 2 = 90, the measure of angle 2 + the measure of angle 3 = 90. Prove: the meausre of angle 1 is congruent to the measure of angle 3.

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.