Splash Screen Today in Geometry Lesson 2.1: Inductive Reasoning Lesson 2.2: Analyze conditional...

Today in Geometry

• Lesson 2.1: Inductive Reasoning

• Lesson 2.2: Analyze conditional statements.

Vocabulary

• Conjecture: An unproven statement that is based on observations

• Inductive reasoning: You use inductive reasoning when you find a pattern in specific cases and then write a conjecture for the general case.

Make a conjecture about the next number based on the pattern.

2, 4, 12, 48, 240

Answer: 1440

Find a pattern:

2 4 12 48 240

×2

The numbers are multiplied by 2, 3, 4, and 5.

Conjecture: The next number will be multiplied by 6. So, it will be or 1440.

×3 ×4 ×5

Make a conjecture about the next number based on the pattern.

Answer: The next number will be

Lesson 2.2: Conditional Statements

Objective: Be able to analyze and verify conditional statements.

Vocabulary

Conditional statement: A conditional statement is a statement that has two parts: a hypothesis and a conclusion. It is written in the if-then form.The “if” part contains the hypothesis and the “then” part contains the conclusion.

Identify the hypothesis and conclusion of the following statement.

If a polygon has 6 sides, then it is a hexagon.

Answer: Hypothesis: a polygon has 6 sidesConclusion: it is a hexagon

Words : If p then q. Symbols: p q

hypothesis conclusion

If a polygon has 6 sides, then it is a hexagon.

Tamika will advance to the next level of play if she completes the maze in her computer game.

Answer: Hypothesis: Tamika completes the maze in her computer gameConclusion: she will advance to the next level of play.

Identify the hypothesis and conclusion of the following statement.

Identify the hypothesis and conclusion of each statement. Then write each statement in if-then form.

a. A polygon with 8 sides is an octagon.

b. An angle that measures 45º is an acute angle.

Answer: Hypothesis: a polygon has 8 sidesConclusion: it is an octagonIf a polygon has 8 sides, then it is an octagon.

Answer: Hypothesis: an angle measures 45ºConclusion: it is an acute angleIf an angle measures 45º, then it is an acute angle.

Related conditionals

They are similar as the conditional statement but not the same.1) Converse: To write the converse of a conditional statement,

exchange the hypothesis and conclusion.

Related conditionals

2) Inverse : To write the inverse of a statement, negate both the hypothesis and the conclusion.

Words: If not p, then not q. Symbols: ~p, then ~q

Write the converse, inverse, and contrapositive of the statement All squares are rectangles.

Conditional: If a shape is a square, then it is a rectangle.

First, write the conditional in if-then form.

Write the converse by switching the hypothesis and conclusion of the conditional.

Converse: If a shape is a rectangle, then it is a square.

Example 4 continued

• Inverse: Negate both the hypothesis and the conclusion.

Hypothesis was: If a shape is a rectangleConclusion was: Then it is a square So inverse is: If a shape is not a square, then it is not a rectangle.

Magazine project

Magazine Project due on October 9th

• The assignment will give you practice using some of the laws of logic in geometry. You will select an advertisement from a magazine as the focus of this subject. Please select something legal and appropriate. You will mount your advertisement on a construction paper. On a separate piece of paper that will take half of the construction paper, you will type and label the following sentences:

• 1) A conditional statement in the if-then form that goes with your add For example: If I use Pantene shampoo, then I will be beautiful

2) The converse of your conditional statement

3) The inverse of your conditional statement

4) The contrapositive of your conditional statement.