Project: Prove It Yourself

Lesson 10 of 10 · 8 min · Free, no account needed

What you will learn

Testing a few shapes makes a claim convincing; only a chain of reasons makes it proved.
A proof that never uses a particular shape holds for every shape, even extreme ones.
One counterexample breaks a claim, and fixing the wording can make it true.

Mathematicians don't just believe. Pick a claim, test it, then make it unbreakable.
Tap the claim you want to work on.
Test your claim with your hands.
Drag the blue points. Record three different shapes.
Three shapes agree. Is the claim proved?
There are infinitely many shapes. Only an argument that never depends on the particular shape can cover them all.
Build the proof of your claim.
Tap blocks to add links. Each must follow from the ones above it. Watch for traps.
Every link uses only facts proved earlier in the course: angle sums, isosceles triangles, similar triangles.
Push it to the edge.
Drag the figure into the two extreme shapes on the list. Your chain sits beside it.
Challenge: "A shape with four equal sides has four right angles."
Break it by dragging a corner. Then fix the wording.
Game: break it or trust it.
Four claims about triangles. Break each one by dragging, or tap Can't break it if you know why it's true. Three lives.
An image model was right on all 100 test photos. Is it proved to work?
Turn the photo and watch what it says.
Find the gap in this proof that MN is half of BC.
One link doesn't follow from anything above it. Tap it, then Check.
Every link must follow from given facts or earlier links. A look at one picture follows from nothing.
Your project card.
Tap it to flip.

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