Teacher: Hello, class. Welcome to math class. Last class, we learned the classification of triangles and learned about different types of triangles. In this lesson, let's continue to understand the triangle and explore the mystery of the interior angle and center of the triangle.

Teacher: In the kingdom of mathematics, there are many kinds of triangles. There are two triangles arguing endlessly this morning. What happened? Let's take a look.

(Play animation: obtuse triangle, acute triangle, right triangle)

Teacher: Students, the shapes and sizes of these three angles are different, so are their degrees the same? We need to study it.

Teacher: This is a triangle, and the three angles of the triangle are its inner angles. For the convenience of research, we often record the three internal angles of a triangle as angle 1, angle 2 and angle 3 respectively, and then the sum of the degrees of these three angles is the sum of the internal angles of the triangle.

Sum of internal angles of triangle: angle 1+ angle 2+ angle 3.

Teacher: How can I know how many degrees the sum of the internal angles of a triangle is?

We can measure it with a protractor. Let's begin our journey of exploration.

Second, independent inquiry.

Activity requirements:

1. Draw several different triangles on white paper, measure the degree of the inner angle, and fill in the form completely.

2. Observe the statistics. What did you find?

Display communication:

Acute triangle: 36 degrees, 74 degrees, 7 1 degree, 18 1 degree.

Acute triangle: 60 degrees, 55 degrees, 65 degrees, 180 degrees.

Obtuse triangle: 1 10 degree, 24 degree, 46 degree, 180 degree.

Right triangle: 90 degrees, 27 degrees, 62 degrees, 179 degrees.

Teacher: As we can see from the table, four triangles with different shapes have been measured. It can be found from the results that the sum of the three internal angles is around 180 degrees, which is close to 180 degrees.

Guess: the sum of the internal angles of the triangle is 180 degrees.

Transition: Some students must have doubts, some are exactly equal to 180 degrees, and some are not. What happened? In fact, there may be errors in the measurement, so the calculated sum is around 180 degrees. It seems that this conjecture needs further verification.

Third, verify the conjecture.

Is there any way to verify your idea? Say and do.

1, (cut and spell)

Teacher: Cut out the three corners of the triangle and put them together. Try all different shapes of triangles.

Teacher: Whether it's an acute triangle, an obtuse triangle or a right triangle, their three internal angles together are a right angle of 180 degrees. In this way, our conjecture has been verified.

2, (10% off, 10% off)

Teacher: Fold the three inner corners of the triangle back and spell it, just to spell a right angle of 180 degrees. A right triangle folds back two acute angles to form a 90-degree right angle.

Folding method: first find the middle of both sides, and then fold down.

3. (Rectangular reasoning)

Teacher: The sum of the internal angles of a rectangle is 90 degrees 4= 180 degrees.

Cut the rectangle into two right triangles according to the diagonal, and then:

Sum of internal angles of right triangle: 360 degrees divided by 2= 180 degrees.

Summary: The sum of the internal angles of the triangle is 180 degrees.

Transition: Just now, through hands-on operation, guessing, verification and exploration, we found the characteristics of the sum of the angles in the triangle and savored it. Is the process of exploration and discovery interesting? Let's go back and start the debate about three triangles. Think about their problems. Regardless of the size of the shape, the sum of the internal angles of the triangle is the same, which is 180 degrees.

Let's solve some practical problems with the sum of the internal angles of the triangle.

Fourth, give it a try.

1. What triangle can it be? (Covered by a corner)

Teacher: Subtract the degree of two known acute angles from the sum of the internal angles of the triangle and 180 degrees, which is equal to the degree of the angle.

180 degrees -30 degrees -40 degrees = 1 10 degrees (obtuse triangle)

2. What triangle could it be? (Two corners are covered)

Teacher: First, find the sum of two covered angles.

180 -70 degrees = 1 10 degrees

1 10 degrees = (? )+(? )

It can be an acute triangle, a right triangle or an obtuse triangle.

Verb (abbreviation for verb) consolidation exercise

1, one point

Cut the triangle below into two triangles along the dotted line. What is the sum of the internal angles of each triangle?

Step 2 fight together

Spell a quadrilateral and a triangle with two identical trigonometric rulers. What are their internal angles and differences?

Step 3 talk about it

Are they right?

Step 4 do the math

Fill in the degrees of the following angles.

Sixth, mathematical stories.

Mathematician: Pascal proved at the age of 12 that "the sum of the internal angles of any triangle is 180 degrees.

Teacher: How did Pascal prove it? Interested students can consult the materials after class, understand Pascal's proof method, and share what they have seen with their relatives and friends. The teacher also hopes that you can learn Pascal's selling spirit, and the teacher also hopes that you can continue to think after class.

Keep thinking:

Try to explore the sum of internal angles of quadrilateral by the method of learning in this lesson.

Conclusion: Please cheer up and dare to challenge yourself. The teacher looks forward to your sharing!