Geometric Proofs & Reasoning
📋 What it is
A proof is a chain of statements, each justified by a definition, postulate or earlier fact, ending at the goal.
🗣️ Coach says
A proof is geometry's argument. You start from what's given, and each step names its reason (a definition or a rule you already know) until you reach the thing you wanted to show. No leaps — every link is justified.
🧠 Memory hook
Every proof line needs a REASON. "Because it looks like it" is never a reason — a rule is.
😂 Giggle
Why was the trapezoid always the mediator?
It had two sides that were on parallel tracks but still brought the other two together!
😲 Whoa!
Euclid's proofs from ~300 BC are still taught today — one of the longest-running pieces of reasoning humans have ever kept using.
✅ Quick check: In a proof, why isn't "it looks equal in my drawing" a valid reason?
Say your answer out loud first — then reveal.
A drawing can be inaccurate; a proof needs a definition, postulate or proven fact as the reason.
Proofs rely on logic, not on the appearance of a sketch.
🧪 Try it! (2 minutes)
Explain to someone why two angles are equal using a reason ("vertical angles are equal"), not "it looks like it".