Geometry

# The Pythagorean Theorem

In a right-angled triangle, the side opposite the right angle is called the **hypotenuse**. The two sides that form the right angle are called **catheti** or legs.

**Pythagorean Theorem**: in a right triangle, the addition of the squares of the lengths of the catheti equals the square of the length of the hypotenuse.

Example 1: If b = 4 and c = 3, find out the hypotenuse.

Example 2: If a = 13 and c = 5, find out the other cathetus.

Example 3: Which is the length of the diagonal of a rectangle with base 24 cm and height 10cm?

**Exercises**:

1.- Could a right triangle have side lengths of 29, 21, and 20 inches?

2.- A boat sails east for 20 km and then it sails north for 5 km. How far is the boat from its starting position?

Solutions: 1.- Yes; 2.- 20.6 km

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