"Pythagorean Theorem" PPT courseware 8

"Pythagorean Theorem" PPT courseware 8

learning target

1. Knowledge and skills

Master the quantitative relationship reflected by the Pythagorean Theorem; be able to use the puzzle method and area method to prove the Pythagorean Theorem; learn to use the Pythagorean Theorem in daily life practice.

2. Process and methods

Understand the Pythagorean Theorem through the process of "observation-conjecture-induction-verification"; learn mathematical thinking methods from the specific to the general.

3. Emotional attitudes and values

Understand the occurrence and development process of mathematical knowledge through experiments, conjectures, puzzles, proofs, etc., learn to cooperate and communicate, experience the fun of inquiry, and enhance the awareness of exploration; feel the long history of the Pythagorean Theorem and stimulate enthusiasm for learning.

Pre-class tutorial

1. Find the length of the unknown side of the following right triangle.

2. Try to talk about the Pythagorean Theorem.

If the lengths of the two right-angled sides of a right triangle are a and b respectively, and the length of the hypotenuse is c, then a2+b2=c2.

Self-learning

1. In Figure 1, Δ ABC is a right triangle, ∠ ACB = 90°.

(1) If each small square grid is a square with side length 1, then what are the lengths of the three sides AC, BC, and AB of Rt ΔABC? What are the areas of the three squares with AC, BC, and AB as sides? How many are each? What is the equivalence relationship between these areas?

(2) If the lengths of the three sides of this right triangle are a, b, and c respectively, how can we use a, b, c to express the relationship between the areas of the three squares in the picture?

2. Figure 2 (1) is a floor paved with square tiles of two colors of the same size.

(1) What is the equivalence relationship between the areas of the three squares marked with white boxes in Figure 2 (1)?

(2) According to Figure 2 (2), can you tell how the equivalence relationship between the areas of squares reflects the relationship between the three sides of Rt ΔABC? Write it out.

collaborative inquiry

Do it yourself: Make right triangle ABC so that ∠C=90°,

AC=6cm　BC= 8cm． (First group)

AC=5cm　BC=12cm. (First group)

AC=9cm　BC=12cm． (First group)

Hands-on measurement: Please use a ruler to measure the length of the hypotenuse of the triangle drawn by your group?

Do some math: What is the relationship between the squares of the three sides of the right triangle your group drew?

Use your brain to guess: Is the sum of the squares of the two right-angled sides of any right triangle equal to the square of the hypotenuse?

Verification experiment

1. Ask each group to take out four prepared congruent right triangles (let the two right-angled sides of the right triangle be a, b, and the hypotenuse c);

2. Can you use these four right triangles to form a square? Give it a try

3. Does the square you put together include a square with hypotenuse c?

4. Can you explain a2+b2=c2 based on the picture you spelled out?

Classroom testing

1. The teacher uses two right triangles to form a trapezoid. Please verify the Pythagorean theorem a2+b2=c2.

2: The known data in the figure represents the area. Find the values ​​of the unknown numbers S1 and S2 representing the area.

3: The known data in the figure represents the side length, and find the values ​​of the unknown numbers x1 and x2 that represent the side length.

4. As shown in the picture, affected by a typhoon, a tree broke 4 meters above the ground. The top of the tree fell 3 meters from the bottom of the tree. How high was the tree before it broke?

Gain insights

1. What did we learn in this lesson?

Through study, we know the famous Pythagorean theorem, master the exploration method from special to general, and also learn the method of puzzle proof.

2. What thoughts or doubts do we have after learning this lesson?

We find that some mathematical conclusions exist in ordinary life and require us to observe, think, and discover with a mathematical perspective.

Homework assignment

1. Complete textbook exercises Group A 1, 2, and 3 (complete independently)

2. Small experiment after class: As shown in the figure, three semicircles are made with the three sides of a right triangle as diameters. What is the relationship between the areas of these three semicircles? Why? (Completed in groups)

3. Preview the Pythagorean Theorem and solve practical problems (complete independently, if you encounter problems, you can communicate with the teacher)

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