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