How do you complete a two column proof?

Know What You’re Up Against: First things first, read the problem carefully. What are you trying to actually prove? What juicy bits of information are they handing you (the “givens”)? Pinpointing these two things is mission-critical.

Draw It Out: If they haven’t already given you a diagram, sketch one yourself! And don’t just draw it – mark it up! Throw on all the known info: congruent angles, equal line segments, parallel lines, right angles… the works. A good visual can make all the difference; trust me, it’s like having a cheat sheet right in front of you.

Column Time: Grab a piece of paper and draw a line right down the middle. Label the left side “Statements” and the right side “Reasons.” Boom. You’re officially organized.

Start with a Gift (the Given, that is): Plop all the “given” information into the “Statements” column. And in the “Reasons” column? Just write “Given.” Easy peasy. This is your starting point, the foundation of your entire proof.

Strategize: Don’t just dive in headfirst! Take a moment to map out your attack. What theorems or definitions seem relevant? How can you use what you know to get to what you need to prove? Sometimes, I even work backward from the “prove” statement to see how I can get there.

Step-by-Step Logic: Now, build your case, one statement at a time. Each statement should flow naturally from the last, like dominoes falling. And for every statement, you must have a reason! Definitions, postulates, properties, proven theorems – these are your ammo. Don’t skip any steps, even if they seem obvious. Trust me, leaving out a step is like leaving a hole in your argument.

Think “If-Then”: This is a pro tip. The “Reasons” column often follows an “if-then” structure. The “if” part of the reason should be somewhere in the statements above, and the “then” part should match the statement directly across from it.

Stick the Landing: Your final statement must be what you were trying to prove in the first place. And the reason? It should be the final, clinching justification that ties everything together. Victory!