"Pythagorean Theorem" PPT courseware 5

Description

"Pythagorean Theorem" PPT courseware 5

learning target

1. Experience the process of exploring and verifying the Pythagorean Theorem, and understand the exploration methods and internal connections of the Pythagorean Theorem.

2. Master the Pythagorean Theorem and be able to use it to solve some practical problems.

Explore the Pythagorean Theorem

(1) In the figure, square A contains small squares, that is, the area of ​​A is unit area.

The area of ​​square B is ____ unit area.

The area of ​​square C is ____ unit area.

(2) In Figure 2, how many small squares are contained in each of squares A, B, and C? What is their area?

(3) Can you find any relationship between the areas of the three squares A, B, and C in Figure 1? What about Figure 2?

Pythagorean theorem

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

The sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse.

Practice in class

1. (2010·Yiwu High School Entrance Examination) In a right triangle, the lengths of the three sides that meet the conditions can be _______. (Just write down a group)

[Analysis] As long as it is the Pythagorean number.

Answer: 3, 4, 5 (anything that meets the meaning of the question is acceptable)

2. The plane flew horizontally in the air. At a certain moment, it happened to fly 3 kilometers above the head of a boy. After 20 seconds, the plane was 5 kilometers away from the head of the boy. How many kilometers did the plane fly during this process? ?

[Analysis] In Rt△ABC,

BC²=5²-3²=16

∵BC>0

∴BC=4

Answer: The distance the plane flew was 4 kilometers.

3. Find the area of ​​a right triangle with a hypotenuse of 17 cm and a right-angled side of 15 cm.

[Analysis] Suppose the length of the other right angle side is x centimeters. From the Pythagorean Theorem:

152+ x2 =172 and x2=172-152=289–225=64

So x=±8 (negative values ​​are rounded off)

So the length of the other right angle side is 8 cm

The area of ​​the right triangle is: 1/2×8×15=60

Summary of class

Through the study of this class, we need to master:

Pythagorean theorem:

The sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse, that is, a²+b²=c²

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Update Time: 2024-07-06

This template belongs to Mathematics courseware People's Education Press Eighth Grade Mathematics Volume 2 industry PPT template

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