"Definition and Proposition" Proof PPT Courseware 4

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"Definition and Proposition" Proof PPT Courseware 4

Generally, a sentence that clearly stipulates the meaning of a name or term is called the definition of the name or term.

For example: 1. "A person with the nationality of the People's Republic of China is called a citizen of the People's Republic of China" is the definition of "a 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";

How to define a noun

Observe the degree and number of terms of the following integers, find their common characteristics, give them names, and define them.

(A)x²-2x-1 (B)2x²+3x+1

(C) x²-2xy+2y² (D) 4a²-4ab+b²

Features: There are three terms A, B, and C, and the highest degree of the term is quadratic.

Please give the definition of the following nouns:

⑴ Irrational numbers: Infinite non-repeating decimals are called irrational numbers.

⑵ Obtuse triangle: A triangle with one obtuse angle is called an obtuse triangle.

⑶Linear function: Generally, a function of the form y=kx+b (k and b are both constants and k≠0) is called a linear function.

Determine whether the following statements are propositions? It is represented by "√", not "×".

1) Are two line segments of equal length equal line segments? ( )

2) Two straight lines intersect, and there is only one intersection point ( )

3) Two unequal angles are not opposite vertex angles ( )

4) The measure of a straight angle is 180 degrees ( )

5) Two equal angles are opposite vertex angles ( )

6) Take the midpoint C of line segment AB; ( )

7) Draw two equal line segments ( )

Indicate the proposition and conclusion of the following propositions

1. If two straight lines intersect, then they have only one intersection point;

Question: Two straight lines intersect

Conclusion: They have only one intersection point

2. If ∠1=∠2, ∠2=∠3, then ∠1=∠3;

Question setting: ∠1=∠2, ∠2=∠3

Conclusion: ∠1=∠3

3. Two straight lines are intercepted by a third straight line. If the interior angles on the same side are complementary, then the two straight lines are parallel;

Question: Two straight lines are intercepted by a third straight line, and the interior angles on the same side are complementary

Conclusion: These two straight lines are parallel

Do it

Point out the conditions and conclusions of the following propositions, and rewrite the form of "if...then...":

⑴ Two triangles whose two sides and their included angles are equal are congruent;

Two triangles are congruent if their sides and angles are equal.

⑵The two acute angles of a right triangle are complementary to each other.

Two angles are complementary if they are acute angles of a right triangle.

What did you learn in this lesson?

1. Definition

Generally, a sentence that clearly stipulates the meaning of a name or term is called the definition of the name or term.

2. Proposition

Generally speaking, sentences that make a correct or incorrect judgment about something are called propositions.

The key to judging whether a sentence is a proposition is: whether a judgment has been made has nothing to do with whether the judgment is correct or not.

The structure of a proposition is proposition (known conditions) and conclusion (matters derived from known conditions).

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Update Time: 2024-09-07

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