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The Pythagorean Theorem is one of the most recognizable theorems in mathematics. This Theorem gives us a relationship among the sides of a right triangle: the sum of the legs squared is equal to the hypotenuse squared. A right triangle is a special type of triangle. It is a triangle with one angle equaling 90 degrees. Now because the measure of the interior angles of a triangle is equal to 180 degrees; we also know that the remaining two angles will sum to be 90 degrees as well. A right triangle has two legs which are the shorter two sides of the triangle, and a hypotenuse which is the longest side of a right triangle, and is located directly across from the right angle. The altitude of a right triangle is equal to a leg in the right triangle. Pythagoras, a Greek mathematician, is credited with the discovery of the Pythagorean Theorem although we know that the Babylonians understood the theorem much earlier. The Pythagorean Theorem can be proven in a variety of ways using: similar triangles, rectangles, and squares. Here is an example of one type of proof for the Pythagorean Theorem . This applet,Pythagorean Puzzles , allows you discover the Pythagorean Theorem by moving pieces of squares and triagnles into a square. This original applet, Pythagorean Theorem allows you to conjecture about the relationships among area of shapes attached to the sides of a right triangle. By using the area of known shapes you can prove that the relationship of the areas follows the Pythagorean Theorem. Thus you can conclude that it is true. Here is an activity plan and a task sheet to go along with the applet. What is the longest side in a right triangle?We define the side of the triangle opposite from the right angle to be the hypotenuse, h. It is the longest side of the three sides of the right triangle. The word "hypotenuse" comes from two Greek words meaning "to stretch", since this is the longest side.
Where would the longest side of a triangle be located?The longest side in a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle. Triangle Inequality: In any triangle, the sum of the lengths of any two sides is greater than the length of the third side. Pythagorean Theorem: In a right triangle with hypotenuse . c , a 2 + b 2 = c 2 .
How do you find the longest part of a right triangle?Use the Pythagorean theorem to calculate the hypotenuse from right triangle sides. Take a square root of sum of squares: c = √(a² + b²)
Why the side across from the right angle has to be the longest side?In a right triangle, the sum of the interior angles will always be 180°. Since a right angle is half that (90°), it has to be the biggest angle in the triangle and the side across from it will always be the longest.
