CHAPTER 9 – LESSON 2 INTRODUCTION TO DEDUCTIVE GEOMETRY (2) 1
Jan 01, 2016
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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.