2.1 Conjectures and Counterexamples

Write a conjecture that describes the pattern in the sequence.

4, 8, 12, 16, 20, ...

• Add 4 each time.

• Multiply by 2 each time.

• Subtract 4 each time.

• Divide by 2 each time.

Find the next item in the sequence.

Workout days: Sunday, Tuesday, Thursday, ...

• Friday

• Saturday

• Monday

• Wednesday

Find the next item in the sequence.

• 
• 
• 
• 

Gabriel started training with the track team five weeks ago. During the first week, he ran 0.5 mile at each practice. The next three weeks he ran 0.75 mile, 1 mile, and 1.25 miles at each practice. If he continues this pattern, how many miles will he be running at each practice during the 7th week?

• 1.5

• 1.75

• 2.0

• 2.25

Make a conjecture.

The product of two and a number, plus one is _____________________.

• always odd.

• always even.

• always negative.

• not possible.

Make a conjecture about the geometric relationship.

∠1 and ∠2 are a linear pair.

• ∠1 + ∠2 = 90

• ∠1 = ∠2

• ∠1 and ∠2 are complementary

• ∠1 + ∠2 = 180

Make a conjecture about the geometric relationship.

Point S is between R and T

• RS = ST

• S is the midpoint of RT

• RS + ST = RT

• Point R is the midpoint

Determine if the statement is true or false. If false, provide a counterexample to show that it is false.

If ∠1 and ∠2 are complementary, then ∠1 = ∠2.

• True

• False, ∠1 = 30 and ∠2 = 60

• False, ∠1 = 45 and ∠2 = 45

Determine if the statement is true or false. If false, provide a counterexample to prove it is false.

If we don't have school, then it is the weekend.

• True

• False; it could be Christmas

• False; it could be Saturday.

• False; it could be Monday.