"Pythagorean Theorem" PPT courseware 9

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"Pythagorean Theorem" PPT courseware 9

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Pythagoras was a famous mathematician in ancient Greece before 2005. One day he discovered that the brick-paved floor of a friend's house reflected a certain quantitative relationship between the three sides of an isosceles right triangle...

What is the relationship between the areas of A, B, and C?

SA+SB=SC

What is the relationship between the three sides of an isosceles right triangle?

The sum of the squares of the two right angle sides is equal to the square of the hypotenuse

(2) Observe Figures 1-2:

Square A contains _____ small squares, that is, the area of ​​A is _____ unit area;

Square B contains _____ small squares, that is, the area of ​​B is _____ unit area;

Square C contains _____ small squares, that is, the area of ​​C is _____ unit area;

Area of ​​A + Area of ​​B = Area of ​​C

Take a guess

What relationships do the three sides of a right triangle satisfy?

Proposition: If the lengths of the two right-angled sides of a right triangle are a and b respectively, and the length of the hypotenuse is c, then a2+b2=c2.

Various expressions of the Pythagorean Theorem:

In RT△ABC, ∠C=90°, the opposite sides of ∠A, ∠B, and ∠C are a, b, and c respectively, then:

c2=a2+b2

a2=c2-b2

b2=c2-a2

Example (1) A 3-meter-long wooden ladder AB is placed on a wall with a height of 2.5 meters (as shown in the picture). How many meters is the distance between the ladder foot and the wall? (Accurate to 0. 01 meters)

Solution: According to the meaning of the question, in Rt△ABO, AB=3 meters, AO=2.5 meters,

From the Pythagorean theorem: AO2+OB2=AB2

∴OB2=AB2-AO2

∴OB=√AB2-AO2

∴OB=√3²-2.5²

OB≈1.66 meters

Answer: The distance between the ladder foot and the wall is 1.66 meters

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"Pythagorean Theorem" PPT courseware 8:

"Pythagorean Theorem" PPT courseware 8 Learning objectives 1. Knowledge and skills Master the quantitative relationship reflected by the Pythagorean theorem; be able to use the puzzle method and area method to prove the Pythagorean theorem; learn to use the Pythagorean theorem in daily life practice. 2. Process and methods Inductive verification through observation and conjecture..

"The Converse Theorem of the Pythagorean Theorem" PPT courseware 3:

"The Converse Theorem of the Pythagorean Theorem" PPT courseware 3 1. Knowledge connection: Question 1. Can you tell what are the characteristics of a right triangle? (1) One angle is a right angle: (2) The right-angled side of 30 degrees is equal to the slope Half of the side; (3) Pythagorean Theorem: The sum of the squares of two right-angled sides is equal to the hypotenuse..

"The Converse Theorem of the Pythagorean Theorem" PPT courseware 2:

"The Converse Theorem of the Pythagorean Theorem" PPT Courseware 2 Review the past and learn the new 1. Explain the Pythagorean Theorem in written language. The sum of the squares of the two right-angled sides of a right triangle is equal to the square of the hypotenuse. 2. State its converse proposition and determine whether its converse proposition is true or false? if..

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Update Time: 2024-10-20

This template belongs to Mathematics courseware Hebei Education Edition Eighth Grade Mathematics Volume 1 industry PPT template

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