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"Application of the Pythagorean Theorem" PPT courseware on the Pythagorean Theorem
Class exercises:
A true or false question. 1. If both sides of ABC are AB=5 and AC=12, then BC=13 ( )
2.ABC’s a=6, b=8, then c=10 ( )
Two fill-in-the-blank questions
1. In ABC, C=90°,
(1) If c=10, a:b=3:4, then a=____, b=___.
(2) If a=9, b=40, then c=______.
2. In ABC, C=90°, if AC=6, CB=8, then the area of ABC is _____, and the height of the hypotenuse is ______.
3． If the length of two equal sides of an isosceles triangle is 10cm and the length of the third side is 16cm, then the height of the third side is ( )
A. 12 cm B. 10 cm C. 8 cm D. 6 cm
As shown in the picture, it is a three-level step. The length, width and height of each step are equal to 55cm, 10cm and 6cm respectively. A and B are the two opposite endpoints of the step. There is an ant at point A. Think of B Order to eat delicious food. Please think about it, this ant starts from point A and climbs along the steps to point B. What is the shortest route?
Solution: The expansion diagram of the steps is as shown in the figure: Connect AB
According to the Pythagorean theorem in Rt△ABC
AB2=BC2+AC2＝552+482＝5329
∴AB=73cm
1. Please complete the following unfinished Pythagorean numbers:
(1) 8, 15, _______; (2) 10, 26, _____．
2. In △ABC, a2+b2=25, a2-b2=7, and c=5, then the height of the largest side is _______.
3． Among the following sets of triangles with three sides, which one is not a right triangle ( ).
A. √3+1, √3-1, 2√2 B． 7, 24, 25
C. 4, 7.5, 8.5 D. 3.5, 4.5, 5.5
Improve “academic ability”
1. As shown in the figure, in the quadrilateral ABCD, ∠BAD=90°, AD=4, AB=3, BC=12, find the area of the square DCEF.
2. It is known that, as shown in the figure, in Rt△ABC, ∠BAC=90°, AB=AC, and D is any point on BC. Verify: BD2+CD2=2AD2.
Enlightenment and reflection
1. What did you gain from the learning activities in this class?
2. Do you have any other thoughts about studying this lesson?
Give it a try:
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?
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