"If Two Straight Lines Are Parallel" Proof PPT Courseware 2

Description

"If Two Straight Lines Are Parallel" Proof PPT Courseware 2

teaching objectives

(1) Teaching knowledge points

1. Proof of the property theorem of parallel lines.

2. General steps of proof.

(2) Ability training requirements

1. Experience exploring the proof of the property theorem of parallel lines. Cultivate students’ ability to observe, analyze and conduct simple logical reasoning.

2. Use symbolic language to express the conditions and conclusions of the three properties of parallel lines by combining graphics. And be able to summarize the general steps of the proof.

(3) Emotional and value requirements

Through joint activities between teachers and students, students can develop their logical thinking ability and become familiar with the format of comprehensive method proofs, thereby stimulating students' initiative in learning.

Judgment of parallel lines

Axiom: The angles of the same angle are equal and the two straight lines are parallel.

∵ ∠1=∠2, ∴ a∥b.

Determination Theorem 1: Internal angles are equal and two straight lines are parallel.

∵ ∠1=∠2, ∴ a∥b.

Decision Theorem 2: Interior angles on the same side are complementary and two straight lines are parallel.

∵∠1+∠2=1800, ∴ a∥b.

By using "Two straight lines are parallel, the angles on the same side are equal" can be proved: Two straight lines are parallel, and the interior angles on the same side are equal. It can also be proved: Two straight lines are parallel, and the interior angles on the same side are complementary.

Think about it: (1) According to "two parallel lines are intercepted by a third straight line, the internal offset angles are equal". Can you make related graphics?

(2) Can you write down what you know and verify based on the graph you made?

(3) Can you talk about the idea of ​​​​the proof?

It is known that, as shown in Figure 6-24, straight lines a∥b, ∠1 and ∠2 are interior angles on the same side of straight lines a and b intercepted by straight line c.

Prove: ∠1+∠2=180°.

Proof: ∵a∥b (known)

∴∠3=∠2 (two straight lines are parallel and have equal angles)

∵∠1+∠3=180° (1 straight angle=180°)

∴∠1+∠2=180° (equivalent substitution)

Proof: ∵a∥b (known)

∴∠3=∠2 (the two straight lines are parallel and the internal offset angles are equal)

∵∠1+∠3=180° (1 straight angle=180°)

∴∠1+∠2=180° (equivalent substitution)

General steps for proof:

Step 1: Draw the graph according to the meaning of the question.

First, draw a graph based on the conditions of the proposition, that is, the known matters, and then mark the conclusion of the proposition, that is, the content of the verification, with symbols on the graph. Also, according to the needs of the proof, mark the necessary letters or symbols on the graph to facilitate the description. or the expression of a reasoning process.

Step 2: Based on the conditions and conclusions, combined with graphics, write down what is known and verified.

The condition of the proposition is written in the language of geometric symbols in known, and the conclusion of the proposition is transformed into the language of geometric symbols in verification.

The third step is to find out the way to prove from what is known after analysis, and write down the proof process.

Under normal circumstances, the analysis process is not required to be written down. In some questions, the graph has been drawn, and the known and verified facts have been written. At this time, you only need to write the "proof" item.

According to the following propositions, draw the graph and combine the graph

Write down what is known and what to prove (do not write down the proof process):

1) Two straight lines perpendicular to the same straight line are parallel;

2) The distance from a point on the bisector of an angle to both sides of the angle is equal;

3) The bisectors of a pair of internal offset angles of two parallel lines are parallel to each other.

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Update Time: 2024-11-18

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