Forms of the Pythagorean theorem
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The Pythagorean Theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The theorem can be expressed algebraically as a2 + b2 = c2, where c is the hypotenuse and a and b are the other two sides. Given the lengths of two sides of a right triangle, the Pythagorean Theorem can be used to calculate the length of the third side.
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Be sure to show the setup and work for each problem. Label answers clearly. Bring any questions to class tomorrow.
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This document summarizes trigonometric formulas for circles, right triangles, oblique triangles, and triangle areas. For circles, it provides formulas for arc length and sector area based on the radius and central angle. For right triangles, it covers the sine, cosine, and tangent definitions and the Pythagorean theorem. For oblique triangles, it introduces the law of cosines and law of sines to solve any triangle given sufficient information. It also provides three formulas for finding a triangle's area based on available side or angle measurements.
10 pythagorean theorem, square roots and irrational numbers
The document discusses rational and irrational numbers. It begins by defining fractions, decimals, and percentages as rational numbers that can be expressed as ratios of whole numbers. It then explains that some quantities, like the length of the diagonal of a 1x1 square, cannot be precisely represented by rational numbers. This length, known as the square root of 2, or √2, is shown to be irrational using the Pythagorean theorem. Most numbers are in fact irrational, requiring infinite decimal expansions. The document concludes by defining square roots and providing examples of evaluating square roots of positive numbers.
Pythagorean theorem powerpoint
1) The Pythagorean theorem states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. It can be used to find the length of any side of a right triangle if the other two sides are known.
2) The distance formula calculates the distance between two points in a plane by using the differences between their x- and y-coordinates, based on the Pythagorean theorem. You find the distance by taking the square root of the sum of the squared differences of the x- and y-coordinates.
3) The example calculates the distance between points (4, -3) and (7, 2) using the distance formula
Coordinate 1.pdf
This document provides information about a book on coordinate geometry. It includes:
- Contact information for the author, Baraka Loibanguti.
- Copyright information stating the book is free to learners and teachers but cannot be sold, reprinted, or posted online without permission.
- An introductory chapter on coordinates and rectangular coordinate systems including defining points using x and y coordinates, naming coordinates, and finding the distance between two points.
- Methods for finding the area of triangles using coordinates and definitions of collinear points.
- A section on finding the angle between two lines using their slopes in the tangent ratio.
PYTHAGOREAN THEOREM
This PPT prepared by Teacher Educator from Thiagarajar College of Preceptors Madurai for B.Ed Trainees.
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Forms of the Pythagorean theorem
- 1. Pythagorean Theorem Forms of the Theorem
- 2. Forms of the Pythagorean Theorem › Pythagorean Theorem Equation Base Form • 𝑎2 + 𝑏2 = 𝑐2 › If the length of both a & b are known, then c can be calculated as: • 𝑐 = 𝑎2 + 𝑏2 › If the length of the hypotenuse c and of one side (a or b) are known, then the length of the other side can be calculated as: • a = 𝑐2 − 𝑏2 or • b = 𝑐2 − 𝑎2
- 3. Forms of the Pythagorean Theorem Cont’d › As pointed out in previous sections, if c denotes the length of the hypotenuse and a and b denotes the lengths of the other two sides, the Pythagorean Theorem can be expressed as the Pythagorean equation: 𝑎2 + 𝑏2 = 𝑐2 › A generalization of this theorem relates the sides of a right triangle in a simple way, so that if lengths of any side of any triangle, given the lengths of the other two sides and the angle between them. If the angle between the other side is a right angle, the law of cosines reduces to the Pythagorean equation. › The Pythagorean equation relates the sides of a right triangle in a simple way, so that if the lengths of any two sides are known the length of the third side can be found. Another corollary of the theorem is that in any right triangle, the hypotenuse is greater than any one of the other sides, but less than their sum.