Teach & case

Help a near-peer reason through the idea — when you explain it, you understand it best — then read the real decision it comes from.

A real case · you decide

Renard and the triangle that looks right

Renard — a student who measured two angles in a careful drawing and wants to call the result proved

The idea in play: proof — a diagram that looks true is not a proof; the givens + theorems are.

Renard drew the figure carefully, put a protractor on it, and got 90° twice. "See — it's a right triangle, proved." But a drawing is one picture of one case, drawn by hand. Does measuring it settle the question for every triangle like it?

A diagram can mislead in two ways: it can be drawn slightly inaccurately, and it can accidentally show a SPECIAL case that isn't true in general. "It looks 90°" and "it measures 90° in this drawing" are observations about the picture, not the theorem.

A proof is a chain from the GIVENS, through definitions and theorems, to the claim — so it holds for every figure satisfying the hypotheses, not just the one on the page. That's the difference between "convincing" and "certain."

Renard's protractor reads 90°, twice. Is the triangle proved to be right-angled?

A step in Renard's write-up says "these two segments are equal (you can see it in the figure)." Is that a valid step?

Renard's whole move is turning "it looks true" into "here's why it must be" — the picture starts the conjecture, and the givens finish the proof.

Build a proof yourself →