"Proposition and Proof" PPT courseware

Description

"Proposition and Proof" PPT courseware

Group discussion and independent inquiry

A new proposition is formed by exchanging ( ) and ( ) of a proposition. If the original proposition is called the original proposition, then this new proposition is called the converse proposition of the original proposition. Such two propositions are called reciprocal propositions.

There are both true and false propositions. To prove that a proposition is false, you only need to cite a counterexample. To prove that a proposition is true, you must start from the conditions of the proposition and base it on the basic facts and definitions that you have learned. , properties and theorems, etc., to conduct well-founded reasoning. This reasoning process is called proof.

Example Prove: Two straight lines parallel to the same straight line are parallel

Known: As shown in the figure, straight lines a, b, c, ａ∥ｃ,

ｂ∥ｃ，

Verify: ａ∥ｂ

Proof: Construct a straight line d that intersects the straight lines a, b, and c respectively.

∵ｽa∥ｃ (known)

∴∠1=∠2 (two straight lines are parallel and have equal angles)

∵b∥ｃ (known)

∴∠2=∠3 (two straight lines are parallel and have equal angles)

∴∠1=∠3 (equivalent substitution)

∴ｽa∥ｽ (the angles are equal and the two straight lines are parallel)

Discussion: 3 minutes

The proof of the proposition described in words above should be carried out according to the following steps:

Step 1: Draw a picture according to the meaning of the question and convert the written language into symbols

Step 2: Write the known verification based on the graph

Step 3: Prove based on basic facts, existing theorems, etc.

What did you learn?

1. Definition of fraction

2. Basic properties of fractions

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"Proposition and Proof" PPT courseware 2:

"Propositions and Proofs" PPT Courseware 2 Review and Thinking: Which propositions are in the following sentences? Which ones are not propositions? And decide whether the following propositions are true or false. (1) The supplementary angles of the same angle are equal. (2) Congruent angles are opposite vertex angles. (3) Pick any point C on the straight line AB. ..

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Update Time: 2024-11-12

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

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