"Properties of Parallel Lines" Intersecting Lines and Parallel Lines PPT Courseware 3

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"Properties of Parallel Lines" Intersecting Lines and Parallel Lines PPT Courseware 3

review review

How to determine parallel lines?

1. Equivalent angles are equal

2. Internal staggered angles are equal

3. Interior angles on the same side are complementary

On the other hand, if two straight lines are parallel, what is the relationship between congruent angles, interior angles, and interior angles on the same side?

in conclusion

Properties of parallel lines 1

Two parallel lines intersected by a third straight line have equal angles.

The abbreviation is: two straight lines are parallel and have equal angles.

Properties of parallel lines 2

Two parallel lines are intercepted by a third straight line, and their interior angles are equal.

The abbreviation is: two straight lines are parallel and their internal offset angles are equal.

Properties of parallel lines 3

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

The abbreviation is: two straight lines are parallel and the interior angles on the same side are complementary.

Use your talents

As shown in the figure in the quadrilateral ABCD, it is known that AB∥CD,

∠B = 600.

① Find the degree of ∠C;

②Can the degree of ∠A be found based on known conditions?

Solution: ① ∵ AB∥CD (known),

∴ ∠B + ∠C= 1800 (the two straight lines are parallel, and the interior angles on the same side are complementary).

And ∵ ∠B = 600 (known),

∴∠C = 1200 (property of equation).

②According to the known conditions of the question, the degree of ∠A cannot be found.

1. Definition: A statement that judges something is called a proposition.

Notice:

(1) As long as a judgment is made on a matter, whether it is correct or not, it is a proposition.

For example: Congruent angles are opposite angles.

(2) If a sentence does not make any judgment about a certain thing, then it is not a proposition.

For example: draw line segment AB=CD.

For some propositions, if the proposition is true, the conclusion must be true; for some propositions, if the proposition is true, the conclusion may not be true.

For example, the proposition: "If a number is divisible by 4, then it is also divisible by 2" is a correct proposition.

For example, the proposition: "If two angles are complementary, then they are adjacent supplementary angles" is a wrong proposition.

Axiom example:

1. Straight line axiom: There is only one straight line passing through two points.

2. Line segment axiom: Among all the lines connecting two points, the line segment is the shortest.

3. Parallel axiom: passing through a point outside the straight line, there is and is only one straight line parallel to the known straight line.

4. Parallel lines determination axiom: If the angles of the same angle are equal, the two straight lines are parallel.

5. Axiom of properties of parallel lines: Two straight lines are parallel and have equal angles.

Class summary

1. Proposition: A statement that judges something is called a proposition.

(1) Correct propositions are called true propositions, and wrong propositions are called false propositions.

(2) The structure of a proposition: A proposition consists of two parts: proposition and conclusion, which can often be written in the form of "if..., then...".

2. Axioms: Propositions that people have summarized in practice for a long time and serve as the basis for judging the truth or falsehood of other propositions are called axioms.

3. Theorem: A proposition that is proved to be correct through reasoning is called a theorem. It can also be used as a basis for continued reasoning.

4. To judge whether a proposition is a true proposition, you can start from the axioms or theorems and prove it by logical reasoning (both axioms and theorems are true propositions);

To judge whether a proposition is false, you only need to give an example to show that the proposition is not true. This method is called giving a counterexample.

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For more information about the PPT courseware "Properties of Parallel Lines Intersecting Lines and Parallel Lines", please click on the Properties of Parallel Lines ppt Intersecting Lines and Parallel Lines ppt tag.

"Properties of Parallel Lines" PPT download:

"Properties of Parallel Lines" PPT Download Part 1 Content: Review Review What are the methods for determining parallel lines? How to identify parallel lines: (1) the angles of the same angles are equal, two straight lines are parallel (2) the internal angles are equal, the two straight lines are parallel (3) the internal angles on the same side are complementary, Two straight lines are parallel...

"Properties of Parallel Lines" PPT:

"Properties of Parallel Lines" PPT Part One Content: Knowledge Review 1. If B=1, according to _______________, we can get AD//BC 2. If 1=D, according to _______________, we can get AB//CD 3. If B+BCD=180, according to___..

"Properties of Parallel Lines" PPT courseware download:

"Properties of Parallel Lines" PPT courseware download Part 1 content: Do a hands-on experiment: Select any two parallel lines a, b on the prepared grid book (1) Draw a straight line c and parallel lines a, b arbitrarily intersect. (2) Choose any pair of co-positioned angles and measure them with a protractor...

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Update Time: 2024-09-03

This template belongs to Mathematics courseware People's Education Press Seventh Grade Mathematics Volume 2 industry PPT template

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