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- Say how each piece of news changes the status of an open conjecture.
- Count toothpicks in rows of squares, state a conjecture for n squares and test it.
- Settle claims about the distance from the origin to points on a line.
- Test a prime number conjecture and explain why it implies a claim about odd numbers.
- Find the angle of regular polygons and test a whole number of degrees conjecture.
- Check a last digit claim for n from 0 to 9 and explain why ten checks are enough.
- Decide if each claim is a for-every or there-is claim and what each fact settles.
- Show a quadrilateral is a counterexample to a conjecture about equal diagonals, then test a repair.
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Conjecture, and why a pattern is not a proof: the lesson ›More Chapter 1 worksheets: Points, lines, planes and the language of proof
- 1.1Axioms, definitions and theorems
- 1.2Points, lines and planes
- 1.3Lines and planes in space
- 1.4The midpoint formula
- 1.5Conjecture, and why a pattern is not a proof
- 1.6Counterexample
- 1.7Inductive reasoning
- 1.8Deductive reasoning
- 1.9Statements and negation
- 1.10Conditionals, converse, inverse, contrapositive
- 1.11Biconditional
- 1.12Converses and biconditional definitions