"Pythagorean Theorem" PPT courseware 6

"Pythagorean Theorem" PPT courseware 6

learning target

Experience the process of exploring the Pythagorean Theorem, feel the idea of ​​combining numbers and shapes, and gain experience in mathematical activities;

Master the Pythagorean Theorem and be able to use the Pythagorean Theorem to solve some problems related to right triangles;

Try to verify the Pythagorean Theorem in various ways and experience the diversity of problem-solving strategies.

(Pythagorean syndrome)

As shown in the picture, there are 8 pieces of the same right-angled triangle paper. Let the right-angled sides be a and b respectively, and the hypotenuse be c; there are two squares with side lengths (a+b). Now I place 4 of the right-angled triangle pieces of paper in the first picture; I place the other 4 right-angled triangle pieces of paper in the second picture. Ask the students to observe what is the relationship between the areas of the three small squares I, II and III in the two figures? Tell us about your findings.

Pythagorean theorem

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

Use mathematical formula to express: c2=a2+b2

Example study

Example 1 As shown in the figure, the height of telephone pole AC is 8m. Pull a steel wire rope from the top A of telephone pole CA and fix the other end to point B on the ground. The length of BC is measured to be 6m. The length of steel wire AB is How many?

Solution In Rt△ABC, ∠C=90°,

AC=8 ,BC=6,

From the Pythagorean theorem, we get

AB2=AC2+BC2

=82+62=100

So AB=√100=10

Therefore, the length of the wire rope is 100 meters.

Example 2 Xiao Ding’s mother bought a 34-inch (86 cm) TV. After Xiao Ding measured the TV screen, he found that the screen was only 70 centimeters long and 50 centimeters wide. He thought the salesperson must have made a mistake. Can you explain why this is?

Solution: ∵702+502=7400

862=7396

Screen diagonal is approximately 86 cm

∴The salesperson was right

Class summary

1) What did we learn in this lesson?

Pythagorean theorem

2) Using the Pythagorean theorem, if the lengths of two sides of a right triangle are known, the other side can be found according to the conditions

3) Understand how to prove the Pythagorean Theorem using the area method

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