Your First Proof | Triangle Congruence

You have to describe a triangle to a friend over the phone so they can cut out an identical cookie cutter. What's the minimum information you need? In this video (high school / college level) you'll see congruence as a perfect overlap by rigid motions, discover the congruence criteria with a compass and straightedge, and write your first formal two-column proofs. In this video you'll learn: ✔ Rigid motions: translation, rotation and reflection ✔ What △ABC ≅ △DEF means, and why the order of the letters matters ✔ SSS, built with a compass ✔ SAS, ASA and AAS (and why AAS reduces to ASA) ✔ Animated counterexample: why SSA and AAA are NOT congruence criteria ✔ A two-column proof of the pons asinorum (Euclid, Book I, Proposition 5) ✔ Proof: every point on the perpendicular bisector is equidistant from the endpoints ✔ 3 examples from easy to exam level (opposite sides of a parallelogram), the trap and a 5-second challenge ✔ Why triangles are rigid: bridges, cranes, power line towers and bikes ✔ The "bridge of donkeys" and Pappus of Alexandria's beautiful proof ⏱️ CHAPTERS 0:00 The cookie cutter over the phone 0:37 Rigid motions: translation, rotation and reflection 1:05 What does congruent (≅) mean? 1:39 SSS with a compass 2:17 SAS, ASA and AAS 3:03 SSA and AAA are NOT criteria (counterexample) 3:48 Proof: the pons asinorum (Euclid I.5) 4:53 Proof: the perpendicular bisector theorem 5:45 Example ladder 7:38 The trap: SSA and AAA 8:12 5-second challenge 8:47 Real world: why triangles are rigid 9:22 3-card recap 9:55 Wow fact: the bridge of donkeys ◀️ Previous: GE-03 · Balance a Triangle on a Pencil | Triangle Centers ▶️ Next: GE-05 · Measure the Great Pyramid With Your Shadow | Similarity 📚 Full playlist: The Architects · Euclidean Geometry 💬 Tell me in the comments: which criterion would you use to prove that the diagonals of a rectangle are equal? 👍 If this helped, hit like and subscribe — new visual math every week. 🇪🇸 ¿Prefieres en español? → @AlgebrayTrigonometria #geometry #triangles #congruence #proofs #math #highschoolmath