Proof as a Chain

Lesson 5 of 10 · 7 min · Free, no account needed

What you will learn

A proof is a chain: every link follows from what is given or from links above it.
"It looks like it" is never a link. Pictures can lie.
Tests can find a mistake; only a proof shows a claim is true for every case.

Your friend says "it's obvious from the picture". Is it?
Which line is longer? Tap your bet.
Now measure.
Drag the ruler onto each line, 0 at the left end.
Prove it instead: if AB = AC, then ∠B = ∠C.
M is the midpoint of BC. Tap blocks to add links. Each one must follow from the ones above it.
Two triangles with three equal sides are congruent (SSS), so every angle of one matches an angle of the other: ∠B matches ∠C.
What makes it a proof.
A proof starts from what is given and from facts already proved.
Each link says therefore: it must follow from links above it. That is deduction.
The last link is the claim. Now it is true for every triangle with AB = AC, not just this picture.
This proof that opposite angles are equal has a rotten link.
Tap the link that isn't a reason. Then pick the block that belongs there.
Your proof: an outside angle equals the two far inside angles.
Drag the top corner to see the numbers change. Then build the chain that works for every shape.
∠1 + ∠2 + ∠3 and ∠3 + ∠4 are both 180°. Remove ∠3 from both and ∠4 = ∠1 + ∠2, whatever the triangle.
Programmers test code. Is a lot of passing tests a proof?
Pip's rule passed every test so far. Run more.
Game: proof race. Every angle of an equilateral triangle is 60°.
All three sides are equal. Build the chain in under 60 seconds, without falling for traps.
Your first proof, on a card.
Tap each line to see what it uses in the figure.

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