"What is a Geometric Proof" PPT courseware

Description

"What is a Geometric Proof" PPT courseware

learning target

1. Understand the meaning of the proof and know the meaning of the theorem.

2. Preliminarily understand the three steps of geometric proof, understand the writing format of geometric proof through examples, and feel that every step of reasoning in the proof process must be well-founded.

Self-study guidance

1. Read page 161 to understand why “basic facts” are stipulated and memorize these “basic facts”.

2. Read page 162 and understand what a proof is? What is a theorem?

3. Read page 163 and summarize what are the steps involved in the process of geometric proof? What are the key points to pay attention to in each step?

Exchange and display

1. Prove: Vertex angles are equal.

Known: As shown in the figure, ∠AOC and ∠BOD are opposite vertex angles.

Prove: ∠AOC=∠BOD.

Prove: ∵ ∠AOC and ∠BOD are opposite vertex angles (known)

∴ ∠AOC+∠AOD=180º

∠AOD+∠BOD=180º (definition of a straight angle)

∴ ∠AOC+∠AOD=∠AOD+∠BOD (equivalent substitution)

∴ ∠AOC=∠BOD (basic property of equation)

2. Complete exercises 1 and 2 on page 165;

3. Fill in the blanks: Question 1 of Exercise 5.3 on page 165.

Instructions and advice

Example 1. Prove: Supplementary angles of the same angle are equal.

Known: As shown in the figure, ∠1 and ∠α are mutually complementary, and ∠2 and ∠α are mutually complementary.

Prove: ∠1= ∠2

Proof: ∵ ∠1 and ∠α are mutually complementary (known)

∴ ∠1+ ∠α=90º (definition of supplementary angle)

∴ ∠1= 90º -∠α (basic property of equation)

And ∵ ∠2 and ∠α are mutually supplementary (known)

∴ ∠2+ ∠α=90º (definition of supplementary angle)

∴ ∠2= 90º -∠α (basic property of equation)

∴ ∠1=∠2 (equivalent substitution)

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"What is a geometric proof" PPT courseware 2:

"What is Geometric Proof" PPT Courseware 2 Teaching Objectives 1. Understand the concepts of original proposition and inverse proposition, be able to identify two mutually inverse propositions, and know that the original proposition is true, but the inverse proposition is not necessarily true. 2. Prove the parallel lines determination theorem. 3. Cultivate students’ reasoning and argumentation..

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Update Time: 2024-09-09

This template belongs to Mathematics courseware Qingdao Edition Eighth Grade Mathematics Volume 1 industry PPT template

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