Practice Work: Geometry Lessons 2.1 - 2.3

Which counterexample shows that the following conjecture is false: “If angle 1 and angle 2 are supplementary, then one of the angles is obtuse”?

• angle 1 = 45° and angle 2 = 45°

• angle 1 = 53° and angle 2 = 127°

• angle 1 = 90° and angle 2 = 90°

• angle 1 = 100° and angle 2 = 80°

Which conjecture is true?

• An even number plus 3 is always even.

• An even number plus 3 is always prime.

• An even number plus 3 is always odd.

• A prime number plus 3 is always even

What is the converse of the conditional statement “If it is January, then it is winter in the United States,” ?

• If it is winter in the United States, then it is January.

• If it is not winter in the United States, then it is not January.

• If it is not winter in the United States, then it is not January.

• Not here

What is the inverse of the conditional statement “If a number is divisible by 6, then it is divisible by 3”?

• If a number is divisible by 3, then it is divisible by 6.

• If a number is not divisible by 6, then it is not divisible by 3

• If a number is not divisible by 3, then it is not divisible by 6.

• If a number is not divisible by 6, then it is divisible by 3.

Given: If one angle of a triangle is a right angle, then the other two angles are both acute. A triangle has a 45 angle.

What conclusion can be drawn?

• One of the other two angles is 90°.

• One of the other two angles is obtuse.

• All three angles are acute.

• No conclusion can be drawn.

Which symbolic statement represents the Law of Syllogism?

• If p ---> q and q ---> r are true statements, then p ---> r is a true statement.

• If p ---> q and p ---> r are true statements, then q ---> r is a true statement.

• If p ---> q and r ---> q are true statements, then q ---> p is a true statement.

• If p ---> r and q ® r are true statements, then p ---> q is a true statement.

Which is a biconditional statement of the conditional statement “If x³ = -1, then x = -1”?

• If x = -1, then x³ = -1.

• x³ = -1 if x = -1.

• x³ = -1 if and only if x = -1.

• x = -1 ---> x³ = -1.

Find the next 2 numbers in the pattern.

1, 2, 3, 5, 8, 13, . . .

• 15, 20

• 20, 33

• 21, 33

• 21, 34

Show that the conjecture is false by finding a counterexample. The difference of two odd numbers is a prime number.

• 23 - 3 = 20

• 35 - 33 = 2

• 57 - 50 = 7

• 48 - 17 = 31

Identify the hypothesis of the statement “If an angle has a

measure less than 90°, then the angle is acute.”

• If an angle has a

  measure less than 90°

• an angle has a

  measure less than 90°

• then the angle is acute

• the angle is acute