1. If you understand the concept of a proposition, you will write it in the form of "If … then ……".
2. Be able to judge the truth of some simple propositions.
3. Continue to use the judgment and nature of parallel lines to solve practical problems.
1. Find out the conditions (topics) and conclusions of the proposition.
2. Comprehensively use the judgment and nature of parallel lines to solve problems.
1. Judge whether a sentence is a proposition.
2. Distinguish the topic and conclusion of the proposition.
3. How to explain that a proposition is false?
Teaching and learning process
First, the self-study process (reverse)
Second, the teaching process:
1. Review and integration:
(1) vertex angles are equal; (2) If, then
(3). Two straight lines are cut by the third straight line. If congruent angles are equal, two straight lines are parallel.
(4) Two straight lines are cut by a third straight line. If the internal dislocation angles are equal, two straight lines are parallel.
⑤. Two straight lines are cut by the third straight line. If they are complementary to the inside angle, then the two straight lines are parallel.
6. Two straight lines are parallel and have the same angle; ⑦. The two straight lines are parallel and the internal dislocation angles are equal;
8. Two straight lines are parallel and complementary;
⑨。 If two lines are parallel to the third line, then the two lines are also parallel to each other.
2. Introduce the topic:
All the above statements are judging one thing. A statement that judges a thing like this is called a proposition.
3. Explore new knowledge:
(1). In mathematics, many propositions consist of two parts: propositions (or known conditions) and conclusions.
(2) the topic is a known thing; A conclusion is a thing derived from a known thing, and such a proposition can often be written in the form of "if ……". The part that begins with "if" is the title, and the part that begins with "then" is the conclusion.
(3). Some propositions are not obvious in the topic and conclusion. You can write it in the form of "if"
(4) All the above propositions are correct. Propositions like this are called true propositions, and some propositions, such as the equality of two angles, are wrong. A false proposition like this is called a false proposition.
5. A true proposition that is proved to be correct by reasoning is called a theorem. Theorem can be used as the basis for further reasoning.
[6]. Judging whether a proposition is true or not can be demonstrated by logical reasoning; To judge whether a proposition is a false proposition, just give an example to show that the proposition is not valid, that is, only give an example that conforms to the proposition and does not conform to the conclusion of the proposition. Mathematically, this method is called "counterexample".
For example, to prove that the proposition "the sum of an acute angle and an obtuse angle is equal to a right angle" is false, just give a counterexample: 60 degrees is an acute angle and 100 degrees is an obtuse angle, but their sum is not 180 degrees.
4. Practice this part through concrete examples.
5. Review the judgment of parallel lines and the comprehensive application of their properties.
As shown in the figure, ∠ 1=∠2,
Description: ∠ 3+∠ 4 = 180.
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