Check out the attached image below to see how the proof table looks like.
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Further explanation:
You start with what we're given, which is the two statements that
- A and B are complementary angles.
- B and C are complementary angles.
We literally copy/paste this into the first box for the "Statements"
From there, we can say A+B = 90 and B+C = 90 due to the definition of what "complementary" means. Complementary angles always add to 90 degrees.
Since A+B = 90 and B+C = 90, the left hand sides can be set equal to one another through the substitution rule. That's how we end up with A+B = B+C on step 3.
Next, we subtract B from both sides to go from A+B = B+C to A = C.
For the last step, we do a bit of a notation change, and the proof is wrapped up.
