"Definition and Proposition" PPT courseware

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"Definition and Proposition" PPT courseware

Self-study guidance

Requirements: Preview textbook P154-156 and solve the following questions: (Time: 2 minutes)

1. What is a definition?

2. What is a proposition?

3. What are the conditions and conclusions of a proposition?

4. What is a true proposition? What is a false proposition?

Cooperate to solve doubts

Generally, a statement used to explain the meaning of a concept is called the definition of the concept.

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 “__________”;

2. "The length of the line segment between two points is called the distance between the two points" is the definition of "__________";

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: A, B, C, and D all have three terms, and the highest degree of the terms is quadratic.

A polynomial with three terms whose highest degree is quadratic is called a quadratic trinomial

Please give the definition of the following nouns:

⑴Even numbers: Numbers that are divisible by 2.

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:

(1) Birds are animals.

(2) The animal is a bird.

(3) Draw an angle equal to the known angle.

(4) The two straight lines are parallel and have equal angles.

(5) Is △ABC an equilateral triangle?

(6) If the square of a certain number is 4, find the number.

(7) The opposite vertex angles are equal.

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 ( )

What is the key to determining whether a sentence is a proposition?

Whether a judgment is made or not has nothing to do with whether the judgment is correct or not.

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

4. If two parallel lines are intercepted by a third straight line, then the internal offset angles are equal;

Question: Two parallel lines are intercepted by a third straight line

Conclusion: internal staggered angles are equal

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

⑴The parallel angles are equal and the two straight lines are parallel;

The condition is: the same angles are equal

The conclusion is: the two straight lines are parallel

Rewritten as: If the parallel angles are equal, then the two straight lines are parallel.

⑵ Two triangles with three equal sides are congruent;

The condition is: the three sides of the two triangles are equal

The conclusion is: these two triangles are congruent

Rewritten as: If two triangles have three corresponding equal sides, then the two triangles are congruent.

(3) In the same triangle, equal angles correspond to equal sides;

The condition is: two angles in the same triangle are equal

The conclusion is: the two sides opposite these two angles are equal

Rewritten as: If two angles in the same triangle are equal, then the sides opposite the two angles are also equal.

(4) The opposite vertex angles are equal.

The condition is: the two angles are opposite vertex angles

The conclusion is: these two angles are equal

Rewritten as: If two angles are opposite vertex angles, then the two angles are equal.

1. Definition

Generally, a statement used to explain the meaning of a concept is called the definition of the concept

2. Proposition

Statements expressing judgments 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 conditions (also called propositions) and conclusions (also called propositions).

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"Definition and Proposition" PPT Courseware 2:

"Definitions and Propositions" PPT Courseware 2 Communication and Discovery In the past, we have explored many mathematical conclusions, some of which are positive and some negative. Can you give a few examples of each? If two angles are opposite vertex angles, then the two angles are congruent. If two angles are not congruent...

"Definition and Proposition" Proof PPT Courseware 5:

"Definitions and Propositions" Proof PPT Courseware 5 It can be seen from this: Communication between people must have a common understanding of certain nouns or terms to proceed normally. For this reason, people have given as detailed a description as possible to the meaning of each noun or term, and made clear regulations...

"Definition and Proposition" Proof PPT Courseware 4:

"Definitions and Propositions" Proof PPT Courseware 4 Generally speaking, a sentence that can clearly stipulate the meaning of a certain 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..

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Update Time: 2024-08-13

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