We will write a proof for the Supplement Theorem. First, let's remember what the Supplement Theorem states.
Supplement Theorem
If two angles form a linear pair, then they are supplementary angles.
Let's make a general diagram that illustrates this situation. We will draw two angles ∠ CBD and ∠ DBA which have a common side.
Here, angles ∠ 1 and ∠ 2 form a linear pair since their non-common sides are opposite rays. Equivalently, the non-common sides form a straight line, so the measure of ∠ ABC is equal to 180^(∘). Using the Angle Addition Postulate we can rewrite m∠ ABC as the sum of two smaller angles.
m∠ 1 + m∠ 2 &= m∠ ABC
&⇓
m∠ 1 + m∠ 2 &= 180
With this information we can concldue that ∠ 1 and ∠ 2, that are in the right-hand side of the equation, form supplementary angles. This statement is also what we wanted to prove.
Alternative Solution
Alternative Solution
We can also write this proof using a two-column proof table. First, using the diagram above, let's write the given information and what we want to prove.
Given:& ∠ ABC form a linear pair.
Prove:& ∠ 1 and ∠ 2 are supplementary.
Now we can proceed with the proof.
