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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.
Example 1-1a Make a conjecture about the next number based on the pattern. 2, 4, 12, 48, 240 Answer: 1440 Find a pattern: ×2×2 The numbers are multiplied by 2, 3, 4, and 5. Conjecture: The next number will be multiplied by 6. So, it will be or ×3×3×4×4×5×5
Example 1-1b Make a conjecture about the next number based on the pattern. Answer: The next number will be
End of Lesson 1
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.
Example 3-1a 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 sides Conclusion: 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.
Example 3-1b 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 game Conclusion: she will advance to the next level of play. Identify the hypothesis and conclusion of the following statement.
Example 3-2c 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 sides Conclusion: it is an octagon If a polygon has 8 sides, then it is an octagon. Answer: Hypothesis: an angle measures 45º Conclusion: it is an acute angle If 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
Example 3-4a 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 rectangle Conclusion 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.