2.3 – Apply Deductive Reasoning. Deductive Reasoning: Using facts, definitions, and logic to form...

2.3 – Apply Deductive Reasoning

Deductive Reasoning: Using facts, definitions, and logic to form a statement

Theorem: A statement that is proved

Law of Detachment: If the hypothesis is true, then conclusion is also true

Given: p q

p is true.

Answer: q is true.

Law of Syllogism:

p q and q rGiven:

Answer: p r

Combine conditional statements

(Cancel the middle)

1. Use the law of detachment to make a valid conclusion in the situation.

If you get a hit, then your baseball team will win. You hit a home run.

Your baseball team will win

1. Use the law of detachment to make a valid conclusion in the situation.

Any time Kendra runs in a cross country race, if she runs a strong race, then she wins. In the cross country race last Saturday, Kendra ran her best race.

Kendra wins

1. Use the law of detachment to make a valid conclusion in the situation.

If Rylee gets promoted, then Callie will also be promoted. Rylee is promoted.

Callie is promoted

2. Use the law of syllogism to make a statement that follows from the pair of statements that are given.

If Moose is hungry when he goes to the pizza shop, then he’ll finish a whole pizza. If Moose eats a whole pizza, then he goes through a pitcher of soda.

If Moose is hungry when he goes to the pizza shop, then he goes through a pitcher of soda

2. Use the law of syllogism to make a statement that follows from the pair of statements that are given.

If you mail the payment by noon, then it will arrive by tomorrow. If your payment arrives by tomorrow, then you won’t be charged a late fee.

If you mail the payment by noon, then you won’t be charged a late fee.

2. Use the law of syllogism to make a statement that follows from the pair of statements that are given.

If a triangle has two angles of 60°, then the triangle is equiangular. If a triangle is equiangular, then it is also equilateral.

If a triangle has two angles of 60°, then it is equilateral.

3. State whether the argument is valid.

Jeff knows that if he does not do his chores in the morning, he will not be allowed to play video games later that same day. Jeff does not do his chores. So Jeff did not play video games.

Valid

2.4 – Use Postulates and Diagrams

Meaning IF THEN

Post 5

Post 6

Through any two distinct points there exists exactly one line.

A line contains at least two points.

Meaning IF THEN

Post 7

Post 8

Through any 3 noncollinear points there exists exactly one plane.

A plane contains at least 3 noncollinear points.

Meaning IF THEN

Post 9

Post 10

If 2 distinct points lie in a plane, then the line containing them lies in the plane.

If 2 distinct planes intersect, their intersection is a line.

1. State the postulate illustrated by the diagram

Through any 3 noncollinear points, there exists exactly one plane

1. State the postulate illustrated by the diagram

A line contains at least two points.

2. Can the statement be assumed by the diagram?

B, C, and D are collinear

No

2. Can the statement be assumed by the diagram?

no

AFECFE

2. Can the statement be assumed by the diagram?

No

BEAC

BFACFE

2. Can the statement be assumed by the diagram?

Yes, vertical angles

2. Can the statement be assumed by the diagram?

and are a linear pair

Yes, are a straight line

CFE AFE

3. Is the following statements true or false?

a. A, B, and C are collinear

True

3. Is the following statements true or false?

b. A, B,C and D are coplanar

True

3. Is the following statements true or false?

c. mABE + mEBC = 180°

True

3. Is the following statements true or false?

False,

AC GC���������������������������������������� ���

No right box!

HW Problem

2.3 # 8

2.3

2.4

90-93

99-102

4-9, 12, 13, 16-19, 25-28

3-5, 9-13, 14-24

Ans: If y > 0, then 2y – 5 5.