Column 1
1.) Find the next item in the pattern: 1, 2, 4, 8, 16, __
32
Identify the Hypothesis and Conclusion
4.) If it is Valentine's Day, then it is February.
Hypothesis: it is Valentine's Day
Conclusion: it is February
Determine if the conjecture is valid or invalid by the Law of Detachment
14) Given: If you pass the final, then you pass the class. You passed the final.
Conjecture: You passed the class.
Valid
Determine if the conjecture is valid or invalid by the Law of Syllogism
16) Given: If a figure is a rhombus, then the figure is a parallelogram. If a figure is a parallelogram, then the figure has two pairs of opposite sides that are parallel.
Conjecture: If a figure is a rhombus, then the figure has two pairs of opposite side that are parallel.
Valid
22.) Identify the property that justifies the statement: <BCA ≅ <BCA
A) Reflexive Property of Congruence
B) Substitution Property of Equality
C) Symmetric Property of Congruence
D) Transitive Property of Congruence
A) Reflexive Property of Congruence
Identify the hypothesis and conclusion of the following conditional statements.
5.) Hypothesis: ____________
Conclusion:_____________
Hypothesis: It does not snow
Conclusion: I will run outside
6.) Write a conditional statement from the following statement: All guitar players are musicians.
If you are a guitar player, then you are a musician.
Determine if the conditional statement is true. If false, give a counterexample.
8.) If two angles are complementary, then the sum of their angles is 90°.
True
23) Identify the property that justifies the statement: If AB = CD, then CD = AB
A) Reflexive Property of Equality
B) Substitution Property of Equality
C) Symmetric Property of Equality
D) Transitive Property of Equality
C) Symmetric Property of Equality
24) Identify the property that justifies the statement: If AW = BX, BX = CY, and CY = DZ, then AW = DZ
A) Reflexive Property of Equality
B) Substitution Property of Equality
C) Symmetric Property of Equality
D) Transitive Property of Equality
D) Transitive Property of Equality
7) Write a conditional statement from the following statement: All dogs have tails.
If there's a dog, then it has a tail.
2a) Look for a pattern using at least 3 examples: The product of 3 negative numbers
-2 x -4 x -6 = -48
-1 x -3 x -5 = -15
-1 x -2 x -3 = -6
2b) Using your results, complete the conjecture: The product of 3 negative numbers is ______
negative
Determine if the following conclusions are based on inductive or deductive reasoning.
12.) Rational numbers can be written as fractions. Irrational numbers cannot be written as fractions. So, 1/2 is a rational number. Which type of reasoning is used to come to this conclusion?
Deductive Reasoning
9.) If it has legs, the it is a beetle. True or False? If false give a counterexample: __________
False, Counterexample: A fly
10) If it is not a leap year, then February had 29 days.
True or False? If False, give counterexample:_______
False, February has 28 days
19) Write the conditional statement and the converse found within the following bi-conditional statement: You are in Yellowstone National Park if and only if you are in Wyoming.
Conditional:________________
Converse:__________________
Conditional: If you are in Yellowstone National Park, then you are in Wyoming.
Converse: If you are in Wyoming, then you are in Yellowstone National Park.
20) For the conditional statement. write the converse and a bi-conditional statement: If a figure is a plane, then it has at least 3 points.
Converse:_________________
Bi-conditional:__________________
Converse: If a figure has at least 3 points, then the figure is a plane.
Bi-conditional: A figure is a plane if and only if it has at least 3 points.
25) Use the transitive property to complete the statement: m<1 = m<2 and m<2 = m<3, then _____
m<1 = m<3
Determine if the conjecture is valid or invalid by the Law of Detachment.
15.) Given: If your parents let you borrow the car, then you will go to the movies with your friend. You went to the movies with your friend.
Conjecture: Your parents let you borrow the car.
Invalid (No conclusion)
11.) Write the converse, inverse, and contrapositive of the following conditional statement: If you are in math class, then you are in Geometry.
Converse: If you are in Geometry, then you are in math class.
Inverse: If you are not in math class, then you are not in Geometry.
Contrapositive: If you are not in Geometry class, then you are not in math.
Draw a conclusion from the given information
18.) Given: If two acute angles form a right angle, then they are complementary. If two angles are complementary, then their measures add up to 90°. Two acute angles form a right angle, therefore.....
Conclusion:
Conclusion: their measures add up to 90°.
21.) Determine if the bi-conditional is true. If false, give a counterexample. (Consider the conditional and converse to help you determine truth-value)
An animal is a bird if and only if it can fly.
False, Counterexample: butterfly, penguin
27.) Given <5 and <6 are complementary, m<5 = 13°
Prove m<6 = 77°
1.) Given <5 and <6 1.) Given
are complementary
2.) m<5 = 13° 2.) Given
3.) m<5 + m<6 = 90 3.) Def of Complementary
4.) 13 + m<6 = 90 4.) Substitution Property
5.) m<6 = 77° 5.) Subtraction Property
26.) Solve the equation and write a justification for each step: 44 - 2(3x + 4) = -18x
Statement: Reason:
1.) 44 - 2(3x + 4) = -18x 1.) Given
2.) 44 - 6x - 8 = -18x 2.) Distribute
3.) 36 - 6x = -18x 3.) Simplify
4.) 36 = -12x 4.) Addition
5.) -3 = x 5.) Division
6.) x = -3 6.) Symmetric Prop