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The Pythagorean Theorem is one of the most importanttheorems in mathematics. It is used in a wide variety of fields, includinggeometry, trigonometry, and physics. The Pythagorean Theorem states that in aright triangle, the square of the hypotenuse is equal to the sum of the squaresof the other two sides.

The best DeltaMath answer to the question "What is the Pythagorean Theorem?"is a comprehensive and informative explanation of the theorem and itsapplications. The answer should include:

A definition of the Pythagorean Theorem

A diagram of a right triangle labeled with the hypotenuseand the other two sides.

A formula for the Pythagorean Theorem

A proof of the Pythagorean Theorem

Examples of how to use the Pythagorean Theorem to solvereal-world problems.

Here is an example of a good Delta Math answer for thequestion "What is the Pythagorean Theorem?":

**The Pythagorean Theorem**

The Pythagorean Theorem is a mathematical formula describing the relationship between a right triangle's sides. It statesthat in a right triangle, the square of the hypotenuse is equal to the sum ofthe squares of the other two sides.

Hypotenuse

Other side

Other side

** ****Formula**

The Pythagorean Theorem can be expressed in the followingformula:

a² + b² = c²

Where:

a and b are the lengths of the other two sides of thetriangle

c is the length of the hypotenuse

** ****Proof**

There are many different proofs of the Pythagorean Theorem.One common proof is based on the following steps:

Draw a square on each side of the triangle.

Divide each square into smaller squares, as shown in thediagram below.

Rearrange the smaller squares from the two smaller squaresinto the larger squares.

Count the number of smaller squares in each square.

**Applications**

The Pythagorean Theorem can be used to solve a wide varietyof real-world problems. For example, it can be used to:

Find the length of a side of a triangle when the other twosides are known.

Find the distance between two points.

Find the area of a triangle.

Find the volume of a pyramid.

Here is an example of how to use the Pythagorean Theorem tosolve a real-world problem:

**Problem:** A ladder is leaning against awall. The bottom of the ladder is 10 feet from the wall, and the top of theladder is 15 feet high. How long is the ladder?

**Solution:**

a² + b² = c²

10² + 15² = c²

c² = 225

c = √225 = 15

Therefore, the ladder is 15 feet long.

The Pythagorean Theorem is a powerful mathematical toolthat can be used to solve a wide variety of problems. By understanding thePythagorean Theorem and its applications, you can better understand mathematics and the world around you.