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# Pythagorean Theorem

Pythagorean Theorem. W ang Qianqian. Audio will be the word in this PowerPoint. Some knowledge of triangle. Right triangle: In △ ABC, when ∠ C=90°, ∠ A+ ∠ B=90 ° When ∠ C=90 ° ，∠ A ，∠ B ，∠ C opposite each sides are a ， b ， c

## Pythagorean Theorem

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### Presentation Transcript

1. Pythagorean Theorem Wang Qianqian

2. Audio will be the word in this PowerPoint Some knowledge of triangle • Right triangle: In △ABC, when∠C=90°, ∠A+∠B=90° • When ∠C=90°，∠A，∠B，∠C opposite each sides are a，b，c • Hypotenuse: the longest side of a right-angled triangle, the side opposite the right angle. A Hypotenuse b c a B C

3. Audio will be the word in this PowerPoint What is Pythagorean Theorem? Pythagorean Theorem: is a relation in Euclidean geometry among the three sides of a right triangle (right-angled triangle). History: The Pythagorean Theorem is named after the Greek mathematician Pythagoras (ca. 570 BC—ca. 495 BC), who by tradition is credited with its discovery and proof. Although it is often argued that knowledge of the theorem predates him.

4. Audio will be the word in this PowerPoint Pythagorean Theorem c=5cm a=3cm b=4cm

5. Audio will be the word in this PowerPoint Recognize right triangle

6. Audio will be the word in this PowerPoint These are not right triangles This is acute triangle. This is obtuse triangle

7. Audio will be the word in this PowerPoint Recognize the Hypotenuse Hypotenuse

8. Audio will be the word in this PowerPoint which one is hypotenuse? A AB，BC and AC, which one is hypotenuse? C B

9. Here is a Rt△ABC, a=3, b=4, and what is the length of c? c Who want to measure it with a ruler? a b

10. As pointed out in the introduction, if c denotes the length of the hypotenuse and a and b denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: If the length of both a and b are known, then c can be calculated as follows: If the length of hypotenuse c and one leg (a or b) are known, then the length of the other leg can be calculated with the following equations: or

11. Example: Question: In Rt△ABC, a=6, b=8, what is the length of c? Answer: as we know, the Pythagorean Theorem shows , We have known a=6, b=8 So =10 A c =? b C B a

12. Class discussion Do you have any questions? Do you know how to use Pythagorean Theorem?

13. Review c a b

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