Geometry U1L1: Conjectures and Counterexamples

Geometry

100

Conjecture: All shapes have 3 sides.

FALSE

Counterexample: square

200

Conjecture: Parallel lines never intersect.

TRUE, by definition of a parallel

Algebra 1

100

Conjecture: If a = b, then b = a.

TRUE, by the symmetric property of equality

200

Conjecture: If  x^2≥9, then x must equal 3. 

FALSE

Counterexample: x = 4 or 5 or 6 or ...

Football

100

Conjecture: Every player on a football team only plays defense.

FALSE:

Counterexamples: Quarterback, Running Back, Offensive Line, Kicker, etc.

200

Conjecture: The Dallas Cowboys have won every game this season (i.e., undefeated)

FALSE: 

Counterexample: The Dallas Cowboys lost yesterday to the Carolina Panthers.

Counterexample: Lost to the Eagles

Counterexample: Lost to the Bears

Counterexample: Tied the Packers

Mr. Cohen

100

Conjecture: Every team that Mr. Cohen roots for is purple. 

FALSE:

Counterexample: Holy Cross is not purple, Iowa State is not purple, Notre Dame is not purple, the MN Wild is not purple...

200

Conjecture: Mr. Cohen only has sisters. He does not have any brothers.

TRUE, my sisters names are Ellie and Anna.

Misc.

100

Conjecture: All bugs have 6 legs. 

FALSE

Counterexample: Spiders have 8 legs

200

Conjecture: There are no students at Holy Cross.

FALSE

Counterexample: Name any student.