"The Property Theorem and Determination Theorem of Parallel Lines" PPT Courseware 2

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"The Property Theorem and Determination Theorem of Parallel Lines" PPT Courseware 2

Review: Determination theorem of parallel lines and planes

If a line outside a plane is parallel to a line in the plane, then the line is parallel to the plane.

Note:

1. The three conditions of the theorem are indispensable.

2. Abbreviation: If the lines are parallel, the lines and surfaces are parallel.

3. The theorem tells us: To prove that lines and planes are parallel, we need to find a straight line in the plane to make the lines parallel.

Thinking: If a straight line is parallel to a plane, is this straight line parallel to all straight lines in the plane?

Thinking: The straight line of the fluorescent tube in the classroom is parallel to the ground. How to draw a straight line on the ground parallel to the straight line of the fluorescent tube?

How to draw parallel lines?

If a straight line is parallel to a plane and the plane passing through the straight line intersects the plane, then the straight line is parallel to the intersection line.

Example 1: There is a piece of wood as shown in the figure. It is known that edge BC is parallel to surface A′C′.

(1) It needs to pass through the wood surface A′B′C′D′

The inner point P and edge BC are used to saw the wood. How should the line be drawn?

(2) What is the relationship between the drawn line and the surface AC?

Example 2: It is known that one of the two parallel straight lines outside the plane is parallel to the plane. Prove that the other one is also parallel to the plane.

summary

Prove the parallel transformation idea:

(1) Parallel axiom

(2) Triangular median line

(3) Parallel lines are proportional to their segments

(4) Corresponding sides of similar triangles are proportional

(5) Opposite sides of a parallelogram are parallel

To prove a //α, by constructing the plane and the plane passing through the straight line a

Intersecting with straight line b, just prove a // b.

Class exercises:

1. The following proposition (where a, b represents a straight line,  represents a plane)

①If a∥b, b∝α, then a∥α

②If a∥α, b∥α, then a∥b

③If a∥b, b∥α, then a∥α

④If a∥α, b∝α, then a∥b

The number of correct propositions is ( )

(A) 0 pieces (B) 1 piece (C) 2 pieces (D) 3 pieces

2. Determine whether the following proposition is correct. If it is correct, please briefly describe the reasons. If it is incorrect, please give a counterexample.

(1) If a and b are two straight lines, and a∥b, then a is parallel to any plane passing through b; ( )

(2) If straight lines a, b and plane α satisfy a∥α, b∥α, then a ∥ b ;( )

(3) If straight lines a, b and plane α satisfy a∥b,a ∥ α,b α, then b∥α;( )

(4) There is only one straight line passing through a point outside the plane and parallel to the plane. ( )

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"The Property Theorem and Determination Theorem of Parallel Lines" PPT courseware 3:

"The Property Theorem and Determination Theorem of Parallel Lines" PPT Courseware 3 Knowledge Review: (1) What is a proposition? How many categories can propositions be divided into? (2) What parts does a proposition consist of? (3) What is the general narrative form of a proposition? Let's talk about it. If two angles are right angles...

"Property Theorem and Determination Theorem of Parallel Lines" PPT courseware:

"The Property Theorem and Determination Theorem of Parallel Lines" PPT Courseware Objective Click Memorize the property theorem and decision theorem of parallel lines Understand the reasoning process of the property theorem and decision theorem of parallel lines, and be able to use axioms to reason out theorems and inferences. Master the basic format of reasoning,...

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Update Time: 2024-10-04

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