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Transcript of Splash Screen Today in Geometry Lesson 2.1: Inductive Reasoning Lesson 2.2: Analyze conditional...
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Today in Geometry
• Lesson 2.1: Inductive Reasoning
• Lesson 2.2: Analyze conditional statements.
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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.
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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
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Make a conjecture about the next number based on the pattern.
Answer: The next number will be
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Lesson 2.2: Conditional Statements
Objective: Be able to analyze and verify conditional statements.
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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Magazine project
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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.