Theme congruent triangles

Teaching content People's Education Edition Nine-year Compulsory Education Junior Middle School Geometry Volume II P2 1 congruent triangles

Teaching purpose and teaching requirements

1, will talk about the congruence of two figures, and will use symbolic language to express the congruence of two triangles.

2. Knowing the related concepts of congruent triangles, we can correctly find out the corresponding vertex, corresponding edge and corresponding angle in congruent triangles.

3. Can speak the nature of congruent triangles.

4. Through the deductive transformation of two overlapping triangles, the activities in different positions between them are presented, from which we can understand and appreciate the idea of graphic transformation and gradually cultivate the consciousness of dynamically learning geometry.

Teaching Emphasis and Difficulties This section focuses on the nature of triangles, and the difficulty is to determine the corresponding elements of congruent triangles.

Teaching tools, multimedia computers or slides

teaching process

First, the introduction of design into teaching:

We often see "the same" graphics around us, such as two identical photos developed from the same negative, window grilles cut from two overlapping papers, and so on. Can you give a few such "identical" examples?

Second, the teaching design:

Question: In geometry, we call the "same" figures listed above "congruent shapes", so how do we give the geometric definition of "congruent shapes"? Yes:

(1) Two graphs with the same shape?

(2) Two figures of equal size?

(3) Two graphs that can completely overlap?

Discussion result: Two figures that can completely coincide are called conformal.

The teacher tells:

(1) Related Concepts of congruent triangles

(2) Representation method of congruent triangles (note that the corresponding positions of the corresponding vertices should be aligned).

[Demonstration experiment design]

(1) Move one of the two overlapping congruent triangles along a straight line with one side, and observe the different positions of the two triangles during the movement. Give a variety of different combination figures, and tell their corresponding vertices, corresponding edges and corresponding angles.

(2) Fold one of the two overlapping congruent triangles by 180 degrees, and observe the positions of the two triangles after folding. Give the combined figures and tell their corresponding vertices, corresponding edges and corresponding angles.

(3) Take a vertex as the center, rotate one of the two overlapping congruent triangles by 0~~ 180 degrees, and observe the different positions of the two triangles during the movement. Give a variety of different combination figures, and tell their corresponding vertices, corresponding edges and corresponding angles.

[Experimental Summary]

1. The key to identify the edges and angles corresponding to congruent triangles is to correctly identify their corresponding vertices.

2. In the above experiment, we transformed two congruent triangles into many geometric figures in different ways. Let's take a closer look. If the positions of two congruent triangles have changed, have their corresponding angles and edges also changed?