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Junior Middle School Mathematics "Judgment of Triangle Congruence AAS"

First, review the test questions

Second, the analysis of test questions

teaching process

(A) the introduction of new courses

Review the learned triangle congruence theorem and its abbreviation (three sides are equal, two sides and their included angles are equal, two angles and their sides are equal) and the combination of conditions that cannot judge triangle congruence (two sides are equal to a diagonal). Guide: If the opposite sides of two angles and one angle are equal, can we judge whether two triangles are congruent? The blackboard writing project "Determination of Triangle Congruence"

(4) Summarize the homework

Summary: Students independently summarize the gains of this lesson.

Homework: Think about whether the three angles are equal, and can you judge the congruence of the triangle? Is there any special congruence criterion for right triangle? Continue to study next class.

blackboard-writing design

Special analysis of national defense

1. What are the methods to judge the congruence of triangles?

Reference answer

There are five ways to determine the consistency of triangles, as follows:

Congruence of a triangle with two equal sides;

Two triangles with equal corners on SAS are the same;

Two equilateral triangles (ASA) are congruent;

The above three judgments belong to nine basic facts of junior high school mathematics.

Use? Corner? And the sum of the angles inside the triangle,

Two angles of an angle side (AAS) are congruent with two triangles with one angle and the opposite side respectively;

The fifth method is only suitable for judging whether two right-angled triangles coincide,

The hypotenuse, hypotenuse of right-angled side (HL) and two right-angled triangles with equal right-angled side are the same.

2. How did you design and explore the judgment theorem of AAS?

Reference answer

The exploration of AAS judgment theorem is divided into two parts: conjecture and proof. In the guessing session, I set up a student activity: given the size of two angles and the length of the opposite side of one angle, let the students draw a triangle that meets the requirements. Finish it independently first, and then work in groups of four. By cutting and overlapping, students find that the four triangles in the group are congruent. Then I selected several groups to show the students. The triangles they made were congruent and overlapped. Students can get the conjecture that AAS can judge the congruence of triangles through personal experience. Then carry out rigorous mathematical proof, guide students to prove AAS with ASA they have learned, infiltrate and transform their ideas, and exercise their knowledge transfer ability.

The reason why I add the guessing link of hands-on operation on the basis of the problem book is because I consider the cognitive law of students. First of all, we can judge the congruence of triangles by perceptual knowledge of AAS through hands-on operation. With the support of experience, we can rationally understand the judgment theorem of AAS through mathematical proof. This is a relatively complete inquiry process or cognitive process.