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CHAPTER 9 – LESSON 2 INTRODUCTION TO DEDUCTIVE GEOMETRY (2)

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CLASS EXPLORATION P.53

Which of the following statements are true / false / can not tell?

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TRUE / FALSE / CANNOT TELL

Sentence 1 2 is an even number.

Answer TRUE

Reason That is the definition

for even number.

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TRUE / FALSE / CANNOT TELL

Sentence 2 Panda have no wings.

Answer TRUE

Reason Pandas are mammals.

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TRUE / FALSE / CANNOT TELL

Sentence 3 There is no sand in desert.

Answer FALSE

Reason Desert made up of sand.

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TRUE / FALSE / CANNOT TELL

Sentence 4 I see clouds in the sky.

Answer CANNOT TELL.

Reason The sky may have no clouds.

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TRUE / FALSE / CANNOT TELL

Sentence 5 Human beings are a kind of animal.

Answer TRUE.

Reason That is a fact.

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TRUE / FALSE / CANNOT TELL

Sentence 6 Do you like Mathematics?

Answer CANNOT TELL.

Reason Someone may love Maths.

Someone may hate Maths.

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TRUE / FALSE / CANNOT TELL

Sentence 7 A triangle must contain a right angle.

Answer FALSE.

Reason E.g. Isosceles triangles.

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TRUE / FALSE / CANNOT TELL

Sentence 8 No Entry.

Answer CANNOT TELL.

Reason We do not know the scenario.

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INTRODUCTION TO DEDUCTIVE REASONING Given Conditions (provided)

Deductive Reasoning (theorems / formulas)

Conclusion Human beings need water.

1. All animals need water.2. Human beings are animals.

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INTRODUCTION TO DEDUCTIVE REASONING Given Conditions (provided)

Deductive Reasoning (theorems / formulas)

Conclusion There will be no school tomorrow.

1. No school on Sundays.2. Tomorrow is Sunday.

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INTRODUCTION TO DEDUCTIVE REASONING Given Conditions (provided)

Deductive Reasoning (theorems / formulas)

Conclusion 8 is divisible by 2.

1. All even numbers are divisible by 2.

2. 8 is an even number.

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INTRODUCTION TO DEDUCTIVE REASONING Given Conditions (provided)

Deductive Reasoning (theorems / formulas)

Conclusion ∆ABC is isosceles.

1. Any triangle with two equal sides

is isosceles. 2. In ∆ABC, AB = AC.

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INTRODUCTION TO DEDUCTIVE REASONING Given Conditions (provided)

Deductive Reasoning (theorems / formulas)

Conclusion An equilateral triangle is isosceles.

1.Any triangle with two equal sides is isosceles.

2.An equilateral triangle has three equal sides.

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CLASS PRACTICE (P.55)

Question 1 Which of the following are statement? Answer

(a) 2 + 3 < 5 ____________(b) Look at the beautiful sky! ____________(c) All plane figures are polygons. ____________

(d) Every prime numbers is an odd number. ____________(e) The sun rises from the west in the morning. ____________(f) The sum of the interior angles of a triangle is 180°. ____________(g) a2+b2 = (a+b)(a–b) ____________

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CLASS PRACTICE (P.56)

Question 2 Write down the conclusion to each of the following using the deductive approach. (a) Given conditions

Deductive ReasoningConclusionThere is no mirage at night.

1. Mirage is a kind of optical illusion created by refraction of sunlight.

2. There is no sunlight at night.

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CLASS PRACTICE (P.56)

Question 2 Write down the conclusion to each of the following using the deductive approach. (b) Given conditions

Deductive ReasoningConclusionOn a horizontal number line, -700 lies to the right of

x.

1. On a horizontal number line, if a number x is larger than another number y, then y lies to the right of x.

2. -700 is less than -7.

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CLASS PRACTICE (P.56)

Question 2 Write down the conclusion to each of the following using the deductive approach. (c) Given conditions

Deductive ReasoningConclusionThe two diagonals of a square are perpendicular to

each other.

1. The two diagonals of a rhombus are perpendicular to each other.

2. A square is a kind of rhombus.

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CLASS PRACTICE (P.56)

Question 2 Write down the conclusion to each of the following using the deductive approach. (d) Given conditions

Deductive ReasoningConclusionThe elephant shown on a computer monitor has

reduced by a scale factor less than 1.

1. A reduced figure has a scale factor less than 1.

2. An elephant shown on a computer monitor is reduced in size.

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AXIOMS, DEFINITIONS, THEOREMS

Axioms (公理 ) Well accepted facts. No need proofs.

Definitions Meaningful statements of some terms and figures.

Theorems Deduced by using axioms and definitions.