"Proof of the Sum of the Interior Angle Theorem of a Triangle" Proof PPT Courseware 2

Description

"Proof of the Sum of the Interior Angle Theorem of a Triangle" Proof PPT Courseware 2

teaching objectives:

Knowledge and skills:

1. Understand the sum of interior angles theorem of a triangle;

2. Master the proof method of the sum of interior angles theorem of a triangle;

3. Be able to use the triangle interior angle sum theorem to prove and solve other related problems.

Process and methods:

1. Prove the sum of the interior angles of a triangle through cutting, spelling and logical reasoning, and understand the role of mathematical symbols in the proof process;

2. Through the teaching of variations of the sum of interior angles theorem of a triangle, you can initially experience the multi-directional nature of mathematical thinking;

3. Through the proof of the sum of the interior angles of a triangle theorem, understand the important thinking method of geometric proof problems---induction method.

Emotions and Attitudes:

1. Cultivate students’ spirit of unity and mutual assistance through hands-on exploration and cooperation among students;

2. Promote personality development, experience the diversity of problem solving, and gain a sense of accomplishment;

3. Enable students to understand logical reasoning, experience the value of mathematical applications, and stimulate students' interest in mathematics.

Cutting and spelling activities:

Cut out corner A and corner B and put them together at corner 1 and corner 2 (note that the cutting line should be a fold line)

Design intention: 1. Through paper-cutting activities, let students initially understand that the sum of the interior angles of a triangle is 180°;

2. Through paper-cutting activities, students can exercise their hands-on ability and cooperative inquiry ability, and cultivate students’ spirit of unity and mutual assistance;

3. Through the display of paper-cutting results and the explanation of ideas, it lays the foundation for logical reasoning to prove the sum of the interior angles of a triangle theorem;

4. Develop students’ language expression ability by asking them to describe their own proof ideas.

Doubts arise again

If the triangle is drawn on an indivisible plane, such as on a blackboard, then how can we prove that the sum of the interior angles of the triangle is 180°?

1. Let the students observe the positional relationship between the line segments in the picture. The teacher guides the students to use auxiliary lines to skillfully transform the three interior angles of the triangle into a straight angle, so that the students can be inspired by the second situation of cutting and spelling using auxiliary lines. The three interior angles of a triangle and the same side angles between two parallel lines provide the necessary conditions for the proof of the theorem.

2. Students discuss proof ideas in groups, group representatives discuss the results, and let student representatives write the proof process on the blackboard.

Prove: Draw the extension line CD of BC, and draw CE∥AB through point C, then

∠1=∠A (the two straight lines are parallel and the internal offset angles are equal)

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

Also ∵∠1+∠2+∠3=180° (definition of a straight angle)

∴ ∠A+∠B+∠ACB=180° (equivalent substitution).

Adding auxiliary lines

① Auxiliary lines are lines that need to be added to the original picture to prove. (Auxiliary lines are usually drawn as dotted lines, and the auxiliary lines are an important part of the proof and must be described first when proving.)

② Its function is to concentrate scattered conditions, reveal hidden conditions, and play a matchmaking role.

③ Adding auxiliary lines can construct new graphics, form new relationships, find a bridge between the known and the unknown, and transform the problem. However, there is no certain rule for adding auxiliary lines. It should be determined according to needs. Pay attention to it when doing questions. Summarize.

Class summary

After studying this section, can you answer the following questions?

1. What is the sum of the angles of a triangle theorem?

2. What are the methods to prove the sum of angles of a triangle theorem?

3. What is the most important thing in proving the sum of angles of a triangle theorem? How?

Activity content: Students summarize in their own words, and students complement each other.

Design intention: Summarize and review to consolidate the knowledge of this lesson and improve students' mastery.

feedback exercise

Basic reproduction:

(1) What is the sum of the two acute angles of a right triangle? What is the degree of an interior angle of an equilateral triangle? Please explain your reasons.

(2) Known: In △ABC, ∠A=600, ∠C=700, points D and E are on AB and AC respectively, and DE//BC. Verify: ∠ADE=500.

power enhanced:

1. Known: As shown in the figure, in Rt △ABC, ∠ACB=900, CD⊥AB. Prove: ∠A= ∠DCB.

Design intention: To understand whether students can flexibly use the sum of interior angles theorem of a triangle.

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For more information about the PPT courseware "Proof of the sum of the interior angles of a triangle theorem", please click on the Proof ppt tag of the proof of the sum of the interior angles of a triangle theorem.

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Update Time: 2024-09-24

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