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"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT Courseware 2
Use the puzzle to verify the Pythagorean Theorem:
1. Prepare four congruent right-angled triangles (let the two right-angled sides of the right-angled triangle be a and b, and the hypotenuse be 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?
Additional exercises:
1. After school, Xiao Hong and Xiao Ying leave school and go home along the southeast and southwest directions respectively. If Xiao Hong and Xiao Ying both walk at a speed of 40 meters/minute, Xiao Hong takes 15 minutes to get home, and Xiao Ying reaches home in 15 minutes. It takes 20 minutes to get home. The distance between Xiaohong’s and Xiaoying’s homes is ( )
A. 600 meters; B. 800 meters; C. 1000 meters; D. Unsure
2. The two right-angled sides of a right triangle are 5 cm and 12 cm respectively. Then the height of the hypotenuse is ( )
A. 6 cm; B. 8 cm; C. 80/13 cm; D. 60/13 cm;
3. The height of the base of an isosceles triangle is 8 and the perimeter is 32. Find the area of this triangle.
Solution: Let this triangle be ABC, the height be AD, let AB be X, then BC is (32-2X), BD is (16-x)
From the Pythagorean theorem:
X²=(16-X)² +8²
That is, X²=256-32X+X² +64
∴X=10
∴ SΔABC=BC•AD/2=2 •6 •8/2=48
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"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT courseware 6:
"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT Courseware 6 Read the textbook and answer the questions (1) Observe Figure 2-1. Square 1 contains ____ small squares, that is, its area is ____ unit area. The area of square 2 is ____ unit area. The area of square 3 is_..
"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT courseware 5:
"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT Courseware 5 The specific method of independent exploration activities before class is: Ask each study group to find and understand as many methods as possible to verify the Pythagorean Theorem from the Internet or books. Analysis of the verification process. And appreciate the first type: to...
"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT courseware 4:
"Exploring the Pythagorean Theorem" Pythagorean Theorem PPT Courseware 4 Question Situation 1. In the last class, we have obtained the Pythagorean Theorem through exploration. What is the content of the Pythagorean Theorem? 2. How to verify the Pythagorean Theorem? According to incomplete statistics, there are more than 400 verification methods. You...