Knowledge and Skills: It is known that the sum of the internal angles of a triangle is 180. It is proved that the sum of the internal angles of a triangle is equal to 180 by the properties of parallel lines and the definition of a straight angle.

Process and method: In the process of proving that the sum of the internal angles of a triangle is 180, we should understand the function of auxiliary lines and use them accurately and normatively.

Emotional attitude and values: experience mathematics in the process of discussion and communication, gain experience in mathematical activities, and improve logical thinking ability.

Second, the difficulties in teaching

Emphasis: the proof of the theorem of triangle interior angle sum.

Difficulties: Using the knowledge learned to prove that the sum of the internal angles of the triangle is180; Function and practice of auxiliary line.

Third, the teaching process

(A) the creation of situations, the introduction of new courses

Question 1: What is the sum of the interior angles of a triangle? How did we get it by cutting?

Default: the sum of the interior angles of the triangle is 180. Cut off the three internal angles of the triangle to form a straight angle, which is 180, so the sum of the internal angles of the triangle is 180.

Teacher writes on the blackboard: drawing

Question 2: Is the conclusion drawn by this method accurate?

Students think, and the teacher emphasizes that sometimes mistakes will occur in the process of cutting and spelling, so this method is not accurate.

(2) Explore new knowledge

Question 3: Look at pictures ① ②. What are the characteristics of the straight line L? Does it exist?

Students answer: the straight line l∨BC in Figure ① and l∨AB in Figure ②. There is no straight line l, we drew it ourselves.

Question 4: The line we added to solve the problem is called auxiliary line, which is not in the original picture. Can you think of a way to prove that the sum of the internal angles of a triangle is equal to 180 with Figure ①?

Default: It can be proved by the nature of parallelism and the definition of flat angle.

Students do their own proofs in the exercise books, and teachers patrol to guide and correct them.

Known: △ABC. Verification: ∠ A+∠ B+∠ C = 180.

Proof: As shown in the figure, the intersection point A is a straight line L, so L∑BC.

∫l∑BC, ∴∠ 2 = ∠∠ 4 (two straight lines are parallel with equal internal angles)

Similarly, ∠3=∠5.

∠∠ 1, ∠4 and ∠5 form a right angle,

∴∠ 1+∠ 4+∠ 5 = 180 (definition of right angle)

∴∠ 1+∠ 2+∠ 3 = 180 (equivalent substitution)

That is, ∠ BAC+∠ B+∠ C = 180.

(3) Consolidate and improve

1. How many right angles does a triangle have at most? Why?

2. How many obtuse angles does a triangle have at most? Why?

3. How many acute angles does a triangle have at most? Why?

(4) Summarize the homework

What do we use to prove the interior angle and theorem of triangle in this lesson? What is the function of the auxiliary line?

Thinking: for the proof of the theorem of triangle interior angle sum, think of other methods to add auxiliary lines, and share them with you next class.

Fourth, blackboard design.

Reflection on the Teaching of verb (abbreviation of verb)