"Can you prove them" Proof PPT courseware

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"Can you prove them" Proof PPT courseware

1. Review and consolidate the relevant content of the proof (1) last semester;

2. Understand the contents of several axioms that are the basis of proof, and master the basic steps and writing format of proof.

3. Go through the process of “exploration – discovery – conjecture – proof”. Be able to use the comprehensive method to prove the relevant property theorems and determination theorems of isosceles triangles.

Focus: Understand the contents of several axioms that are the basis of proof, and master the basic steps and writing format of proof.

Difficulty: Be able to prove the relevant property theorems and determination theorems of isosceles triangles using the comprehensive method.

Axioms, Theorems and Proofs

1. Two straight lines are intercepted by a third straight line. If the angles are equal, then the two straight lines are parallel;

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

3. Two triangles with equal angles are congruent;

4. Two triangles whose two angles and their included sides are equal are congruent;

5. Two triangles with three equal sides are congruent;

6. The corresponding sides of congruent triangles are equal and the corresponding angles are equal.

[Sum of interior angles of a triangle theorem] The sum of the three interior angles of a triangle is equal to 180°.

In △ABC, ∠A+∠B+∠C=180°.

Several deformations of ∠A+∠B+∠C=180o: ∠A=180o –(∠B+∠C). ∠B=180o –(∠A+∠C). ∠C=180o –(∠A+∠B). ∠ A+∠B=180o –∠C. ∠B+∠C=180o –∠A. ∠A+∠C=180o –∠B.

The axioms, theorems and the conclusions (inferences) derived directly from them can be directly used in the future.

General steps to prove a proposition:

(1) Understand the meaning of the question: distinguish the conditions of the proposition (known) and the conclusion (verification);

(2) Draw graphics according to the meaning of the question;

(3) Combine graphics and use symbolic language to write “known” and “verified”;

(4) Analyze the meaning of the question and explore the proof ideas (lead from "cause" to "effect", and use "effect" to find "cause");

(5) Based on the idea, use mathematical symbols and mathematical language to clearly write out the proof process;

(6) Check whether the expression process is correct and complete.

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Update Time: 2024-11-22

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