"Definition and Proposition" Proof of Parallel Lines PPT Courseware 2

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"Definition and Proposition" Proof of Parallel Lines PPT Courseware 2

Review together

1. The conclusions drawn from observations, conjectures, measurements, and experiments may not all be correct, so one must make step-by-step, well-founded inferences, that is, proofs.

2. Methods of proof: positive proof (established) and counterexample (not established).

What is a definition?

To describe and clearly specify the meaning of names and terms is to give their definitions. For example:

(1) "Persons with the nationality of the People's Republic of China are called citizens of the People's Republic of China" is the definition of "citizen of the People's Republic of China"

(2) "The length of the line segment between two points is called the distance between the two points" is the definition of "the distance between the two points"

(3) "A quadrilateral with two sets of opposite sides that are parallel is called a parallelogram" is the definition of "parallelogram"

A sentence that judges something is called a proposition. For example:

(1) Pandas have no wings.

(2) Any triangle must have right angles.

(3) The opposite vertex angles are equal.

(4) No matter what kind of natural number it is, the value of the formula is a prime number.

(5) If two straight lines are parallel to a third straight line, then the two straight lines are also parallel to each other.

Summary and expansion

1. Definition: Describe the meaning of names and terms and make clear provisions, that is, give their definitions.

2. The definition of proposition: A sentence that judges one thing is called a proposition.

3. The structure of a proposition: Each proposition consists of two parts: conditions and conclusions. Conditions are known matters, and conclusions are matters inferred from the already known matters.

4. Characteristics of propositions: Generally speaking, propositions can be written in the form of "if..., then...", where the part introduced by "if" is the condition, and the part introduced by "then" is the conclusion.

5. Classification of propositions: true propositions and false propositions (judgment is a proposition).

Starting from these axioms, it is possible to prove the conclusions already explored. For example, we can prove the following theorem;

Theorem The supplementary angles of same angles (congruent angles) are equal

Theorem: Supplementary angles of same angles (congruent angles) are equal

Theorem Vertex angles are equal

Theorem The sum of any two sides of a triangle is greater than the third side

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For more information about the PPT courseware "Proof, Definition and Proposition of Parallel Lines", please click on the PPT Definition and Proposition of Proof of Parallel Lines tab.

"Definition and Proposition" Proof of Parallel Lines PPT Download:

"Definition and Proposition" Proof of Parallel Lines PPT download, 12 pages in total. Part One: Basic Knowledge Points Knowledge Point 1 Definition and Proposition 1. The following sentences belong to the definition (D) A. Two points determine a straight line B. Two parallel lines are intercepted by a straight line..

"Definition and Proposition" Proof of Parallel Lines PPT Courseware (Lesson 2):

"Definitions and Propositions" Proof of Parallel Lines PPT courseware (Lesson 2), 21 pages in total. The first part of the content: Learning objectives, theorems and axioms, proof... ... Definitions and propositions PPT, the second part of the content: Understanding new knowledge, knowledge points, theorems and axioms 1. In fact, in...

"Definition and Proposition" Proof of Parallel Lines PPT Courseware (Lesson 1):

"Definitions and Propositions" Proof of Parallel Lines PPT courseware (Lesson 1), 24 pages in total. The first part of the content: Learning objectives, definitions, propositions and the composition of propositions, the classification of propositions... Definition and propositions PPT, the second part of the content: Understanding new knowledge, knowledge points, determination...

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Update Time: 2024-10-03

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