"How Ants Get Closest" PPT Courseware on Pythagorean Theorem

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"How Ants Get Closest" PPT Courseware on Pythagorean Theorem

problem situation

On a cylindrical stone bench, if Xiao Ming leaves a little food at place B while eating, and an ant at place A happens to capture this information, so it wants to crawl from place A to place B, what do you think? Think about it, how do ants get closer?

Do it

Uncle Li wanted to test whether the sides AD and BC on the front of the sculpture base were perpendicular to the bottom side AB respectively, but he only brought a tape measure with him.

(1) Can you find a way to complete the task for him?

(2) Uncle Li measured that the length of AD is 30 cm, the length of AB is 40 cm, and the length of BD is 50 cm. Is side AD perpendicular to side AB? Why?

(3) Xiao Ming only has a scale with a length of 20 cm with him. Can he have a way to check whether side AD is perpendicular to side AB? What about side BC and side AB?

1. As shown in the figure, there is an ant at vertex A of a cube with an edge length of 10 cm. Now it wants to crawl to vertex B. It is known that the ant crawls at a speed of 1 cm/second, and the speed remains unchanged. Can the ant crawl? Climb from A to B in 20 seconds?

2. An interesting question is recorded in the ancient Chinese mathematics work "Nine Chapters of Arithmetic". The meaning of this question is: There is a pool, the water surface is a square with a side length of 10 feet, and there is a new reed in the center of the pool. It is 1 foot above the water surface. If this reed is pulled vertically toward the shore, and its top reaches the water surface of the shore, what are the depth of the pool and the length of the reed?

Solution: Suppose the water depth AC of the pool is x feet, then the length of this reed is

AD=AB=(x+1) feet,

In right triangle ABC, BC=5 feet

From the Pythagorean theorem: BC²+AC²=AB²

That is 5²+ x²= (x+1)²

25+ x²= x²+2 x+1,

2x=24,

∴ x=12, x+1=13

Answer: The water in the pool is 12 feet deep, and the reed is 13 feet long.

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"How Ants Get Closest" PPT Courseware 2 of Pythagorean Theorem:

"How Ants Get Closest" PPT Courseware 2 of Pythagorean Theorem 2 Do you know? 1. Do you know the content of the Pythagorean Theorem? 2. The three sides of a triangle are a, b, c (ca, b). How to determine whether it is a right triangle? This morning at 7:00, I set off from home with 1...

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Update Time: 2024-11-22

This template belongs to Mathematics courseware Beijing Normal University eighth grade first volume mathematics industry PPT template

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