"Pay attention to the exterior angles of the triangle" Proof PPT courseware 2

Description

"Pay attention to the exterior angles of the triangle" Proof PPT courseware 2

teaching objectives

1. Knowledge and skills: Understand the definition of the exterior angles of a triangle and be able to find the exterior angles of a triangle in any triangle;

2. Process and methods: The ability to diversify thinking and flexibly use knowledge to solve practical problems while experiencing multiple changes in one question and multiple solutions to each question;

3. Emotional attitudes and values: Through the activities of exploring the inference of the sum of the interior angles of a triangle theorem, students can broaden their problem-solving ideas and improve their problem-solving abilities.

Teaching focus and difficulties

This lesson introduces the concept of exterior angles of triangles, explores and proves several theorems related to exterior angles of triangles, and uses them to solve some simple problems. Relatively speaking, the concept of exterior angles is relatively simple, so I think the focus is on using them to solve Problems, while the difficulty is to develop students' reasoning skills in solving problems.

Question 1. Introduce students to the exterior angles of a triangle, and let students identify their differences and similarities from ∠1 and ∠2 in the figure, and determine which angle is the exterior angle of the triangle. At this point, we further ask: What are the relationships between the exterior angles and interior angles of a triangle?

Question 2. Textbook example P212 and its modification (as shown on the right above)

(1) ∠ACD is an exterior angle of △ABC. What is its relationship with other angles in the figure? Can you prove your conclusion?

(2) Is ∠ACD greater than ∠ABC? Why?

(3) Is ∠ACD = ∠B + ∠ACB? Why?

Explore new knowledge

Example 1. It is known that ∠B=50°, ∠CFD=80° and ∠D=20°. Find: the degree of ∠A.

Example 2. Observe the graphics and answer the questions

(1) ∠AED is the exterior angle of ____

∠ACD is the exterior angle of ____

(2) ∠AED =____+____

∠ACD =____+____

(3)∠AED＞______

∠ACD >______

(4) ∠AFD is the exterior angle of ______

(5)∠AFD =____+____

(6)∠AFD＞______

(7)∠AFD =____+____+____

Teaching reflection

The teaching design of this lesson strives to have the following features:

(1) Fully tap students’ potential, demonstrate students’ thinking processes, and embody the theme of “students are the masters of learning”;

(2) From the specific to the general, from incomplete induction to reasonable reasoning, it demonstrates a complete thinking process;

(3) Try to avoid the monotony of teaching as much as possible in the entire teaching, so we arrange training with multiple solutions to one question to create situations for divergent thinking and mobilize students' great enthusiasm for learning.

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For more information about the PPT courseware "Prove Concern about the Exterior Angle of a Triangle", please click the Prove ppt Concern about the Exterior Angle of a Triangle ppt tag.

"Focus on the exterior angles of a triangle" Proof PPT courseware 4:

"Pay attention to the exterior angles of triangles" Proof PPT courseware 4 Self-study tips As shown in the figure: 1 is an exterior angle of △ABC. What are the characteristics of the vertices and sides of 1 and 1? 2. Can you draw all the exterior angles of △ABC? 3. What is the relationship between 1 and other angles in the picture? Can prove your conclusion...

"Focus on the exterior angles of a triangle" Proof PPT Courseware 3:

"Focus on the Exterior Angle of a Triangle" Proof PPT Courseware 3 The sum of the interior angles of a triangle theorem The sum of the interior angles of a triangle theorem The sum of the three interior angles of a triangle is equal to 180. Several variations of A+B+C=180 in △ABC. A+B+C=1800: A=180 (B+C). B=180(A+C). C=180(A+B)...

"Focus on the exterior angles of a triangle" proof PPT courseware:

"Focus on the Exterior Angle of a Triangle" Proof PPT courseware exploration and thinking as shown in the figure. 1 is an exterior angle of △ABC. What is the relationship between 1 and other angles in the figure? 1+4=180; 12; 13; 1=2+3. Can prove What is your conclusion? Proof: ∵2+3+4=180 (Sum of interior angles of a triangle theorem)..

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Update Time: 2024-11-23

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