*The theorem can be generalized in various ways, including higher-dimensional spaces, to spaces that are not Euclidean, to objects that are not right triangles, and indeed, to objects that are not triangles at all, but n-dimensional solids.*

You may want to watch the animation a few times to understand what is happening.

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The large square is divided into a left and right rectangle.

A triangle is constructed that has half the area of the left rectangle.

This argument is followed by a similar version for the right rectangle and the remaining square.

Putting the two rectangles together to reform the square on the hypotenuse, its area is the same as the sum of the area of the other two squares. Let A, B, C be the vertices of a right triangle, with a right angle at A.

Let ABC represent a right triangle, with the right angle located at C, as shown on the figure.

Draw the altitude from point C, and call H its intersection with the side AB.

Then another triangle is constructed that has half the area of the square on the left-most side.

These two triangles are shown to be congruent, proving this square has the same area as the left rectangle.

## Comments Pythagoras Problem Solving

## Pythagorean Theorem calculator - Basic mathematics

The Pythagorean Theorem calculator will help you to solve Pythagorean problems with ease. Note that the triangle below is only a representation of a triangle. Your triangle may have a different shape, but it has to be a right triangle.…

## Solving Problems Involving the Pythagorean Theorem

Draw a right triangle and then read through the problems again to determine the length of the legs and the hypotenuse. Step 2 Use the Pythagorean Theorem a 2 + b 2 = c 2 to write an equation to be solved. Remember that a and b are the legs and c is the hypotenuse the longest side or the side opposite the 90º angle.…

## Math Practice Problems - Pythagorean Theorem

Pythagorean Theorem - Sample Math Practice Problems The math problems below can be generated by MathScore.com, a math practice program for schools and individual families. References to complexity and mode refer to the overall difficulty of the problems as they appear in the main program. In the main program, all problems are automatically.…

## Real life Pythagoras Problems - TES Resources

A selection of problem cards with real life Pythagoras problems. Most cards require students to find the length of a shorter side of a triangle. The problems range in difficulty Qs 1, 2, 6, 7 are simple, Qs 4, 5 are more complex Qs 3 and 8 are challe.…

## Pythagorean Theorem Word Problems examples, solutions.

How to use the Pythagorean Theorem to solve Word Problems, how to solve different types of word problems using the Pythagorean Theorem, examples and step by step solutions, real life Pythagorean Theorem word problems, questions and answers, grade 9, grade 8…

## Pythagorean theorem word problems - Basic mathematics

Pythagorean problem # 1 John leaves school to go home. He walks 6 blocks North and then 8 blocks west. How far is John from the school? Here is how you can model this situation…

## Pythagorean Theorem Word Problems Worksheet

Pythagorean Theorem Word Problems Worksheet Worksheet given in this section is much useful to the students who would like to practice solving word problems on the Pythagorean theorem. Before look at the worksheet, if you want to know more about the Pythagorean Theorem, Please click here. Pythagorean Theorem Word Problems Worksheet - Questions…

## Pythagorean Theorem Word Problems Worksheets

Most worksheets contain between eight and ten problems. When finished with this set of worksheets, students will be able to solve word problems that require them to use the Pythagorean Theorem. These worksheets explain how to solve word problems using the Pythagorean Theorem. Sample problems are solved and practice problems are provided.…

## Pythagoras Theorem - Math Is Fun

It is called "Pythagoras' Theorem" and can be written in one short equation a 2 + b 2 = c 2. Note c is the longest side of the triangle; a and b are the other two sides ; Definition. The longest side of the triangle is called the "hypotenuse", so the formal definition is…

## How to Use the Pythagorean Theorem. Step By Step Examples and.

Use the Pythagorean theorem to calculate the value of X. Round your answer to the nearest hundredth. Remember our steps for how to use this theorem. This problems is like example 2 because we are solving for one of the legs.…