Final Exam Reiview #4 Honors Geometry

What conclusion can be drawn from the following statements?
If the sun is shining, then it is a beautiful day.  
If it is a beautiful day, then we will have a picnic.

• If the sun is shining, then it is a beautiful day.
• If it is a beautiful day, then the sun is shining.
• If the sun is shining, then we will go on a picnic.
• If we go on a picnic, then the sun is shining.

Tags

CCSS.RI.8.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.11-12.2

CCSS.RI.9-10.1

Using the Law of Syllogism, which of the following completes the statement to form a valid conclusion?
If it is snowing heavily, then school will be canceled.
If school is canceled, the big test will not be given today.
It is snowing heavily, then...

• Look out for the snowplows while driving to school.
• The big test will not be given today.
• The roads will be hard to drive on.
• You should call the school to see if school is canceled.

Tags

CCSS.RI.8.1

CCSS.RL.8.1

CCSS.RL.9-10.1

CCSS.RI.8.8

CCSS.RL.11-12.1

(1) If you drive safely, then the life you save may be your own.
(2) AJ drives safely.
(3)  The life AJ saves may be his own.
Is statement (3) logical given the Law of Detachment, Syllogism, Contrapositive, or is it invalid?

• Law of Detachment
• Law of Syllogism
• Law of Contrapositive
• invalid

(1) If a figure is a square, then it is a polygon.
(2) Figure A is a polygon.
(3)  ???????
What belongs in line 3?

• Figure A is a polygon.
• Figure A is a circle.
• Figure A is a square.
• invalid; nothing belongs in line 3

Tags

CCSS.2.G.A.1

p→q
q→r
∴p→r
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

p→q
p
∴q
Which law is modeled?

• Law of Syllogism
• Law of Detachment
• Law of Contrapositive
• Law of Shannon

If an angle is 40⁰, then it is acute.
∠A is 40⁰.
Using the Law of Detachment, what is the logical statement to conclude?

• ∠A is complementary to ∠B
• ∠A is acute.
• ∠A is obtuse.
• ∠A is 40⁰

Using the Law of Detachment, what can you conclude?
If x has a value of 4, then 2x has a value of 8.
The value of x is 4.

• x = 4
• no conclusion can be made
• 2x does not have a value of 8
• 2x has a value of 8

What is the converse of the statement:
If an animal is a dog, then it does not moo.  

• If an animal is not a dog, then it does moo
• If an animal can moo, then it is not a dog
• If an animal does not moo, then it is a dog
• An animal is a dog if and only if it can moo

Tags

CCSS.RL.11-12.9

CCSS.RL.6.3

CCSS.RL.7.3

CCSS.RL.8.3

CCSS.RL.9-10.3

Which law of logic is used in the argument:

If I buy a dress, then I won't get chips.

I bought a dress.

Therefore, I won't get chips.

• Law of Detachment

• Law of Contrapositive

• Law of Syllogism

• Law of Biconditional