Deductive Reasoning (Day 2)

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.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

Which is a valid conclusion from these statements?
If a quadrilateral is a rhombus, then it is a parallelogram.
If a quadrilateral is a parallelogram, then its opposite angles are congruent.

• Opposite angles of a quadrilateral are congruent
• Opposite angles of a rhombus are congruent
• Every quadrilateral is a rhombus
• Every parallelogram is a rhombus

Tags

CCSS.HSG.CO.C.11

Which statement is a valid conclusion based on the argument?
If a polygon is a regular pentagon, then the polygon has exactly five congruent angles.
The polygon is a regular pentagon.

• Therefore, the polygon is a rectangle.
• Therefore, the polygon is a regular quadrilateral.
• Therefore, the polygon has exactly five congruent angles.
• Therefore, the polygon has congruent sides.

Tags

CCSS.HSG.CO.C.11

(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

Use Law of Syllogism to make a conclusion.
If the perimeter of a square is 20 ft, then the length of a side is 5 ft.
If the length of a side of a square is 5 ft, then the area is 25 ft².

• If the side of a square is 5 ft, then the perimeter is 20 ft.
• If the perimeter of a square is 20 ft, then the area is 25 ft²
• If the area of a square is 25 ft², then the side length is 5 ft. 
• If the are of a square is 25 ft², then the perimeter is 20 ft.

Write the if-then statement that follows from the pair of true statements. If Todd goes to the movies, then Sarah will go to the movies.  If Chris goes to the movies, then Todd will go to the movies.

• If Chris goes to the movies, then Sarah will go to the movies.
• If Todd goes to the movies, then Chris will go to the movies.
• If Sarah goes to the movies, then Chris will go to the movies.
• If Chris goes to the movies, then Todd will go to the movies.

Tags

CCSS.RI.11-12.2

CCSS.RI.8.1

CCSS.RI.9-10.1

CCSS.RL.11-12.1

CCSS.RL.9-10.1

What can be concluded from the following statements?
If Tom goes fishing then he brings a pole.
If Tom brings his pole then he catches a fish.

• If Tom goes fishing then he catches a fish.
• If Tom brings his pole then he goes fishing
•  If Tom catches a fish then he brought his pole.
• If Tom brings his pole then he catches a fish.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

Which of the following statements is valid based on the given scenario?
If Jason plays basketball, then Steve sits on the bench.  
If Steve sits on the bench, then Ronald starts at center.  

• If Steve sits on the bench then Jason plays basketball.
• If Ronald starts at center then Jason plays basketball.
• If Steve sits the bench then Ronald does not start at center.
• If Jason plays basketball then Ronald starts at center.

Tags

CCSS.RI.8.1

CCSS.RI.8.8

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

By the Law of Detachment, what can you conclude from the statement? 
If two planes intersect, then their intersection is a line.
Planes S and T intersect.

• their intersection is a line
• their intersection is a point
• no conclusion can be made
• the planes are parallel

Use the Law of Detachment to determine what you can conclude from the given information, if possible.

If you passed the final, then you pass the class. You passed the final.

• You passed the class.

• You didn't pass the class

• Not possible

Tags

CCSS.L.2.1F

CCSS.L.8.1C

CCSS.L.8.3A