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: 

a*1=a

TRUE, by the identity property of multiplication.

200

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

FALSE

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

Football

100

Conjecture: The only football team in Texas is the Dallas Cowboys. 

FALSE

counterexamples: Houston Texans, HC knights, University of Texas Longhorns, etc. 

200

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

FALSE:

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

Mr. Cohen

100

Conjecture: Mr. Cohen does not root for any sports teams. 

FALSE:

Counterexample: Mr. Cohen roots for Holy Cross sports teams, Iowa State sports teams, Notre Dame sports teams, and MN sports teams...

200

Conjecture: Mr. Cohen recently graduated from college. 

TRUE, Mr. Cohen graduated from Notre Dame this Spring/Summer. 

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.