3-4-5 triangle
A 3-4-5 triangle is a special type of right triangle
A 3-4-5 triangle is a special type of right triangle. In a right triangle, one of the angles is a right angle, which measures 90 degrees. A 3-4-5 triangle specifically refers to the lengths of its sides, where one side is of length 3 units, another side is 4 units, and the third side is 5 units.
To understand why this is a right triangle, we can use the Pythagorean theorem. According to the Pythagorean theorem, in any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In the case of a 3-4-5 triangle, we can check if it satisfies the Pythagorean theorem. Let’s label the sides: the side of length 3 will be ‘a’, the side of length 4 will be ‘b’, and the side of length 5 (the hypotenuse) will be ‘c’.
By applying the Pythagorean theorem, we have:
a^2 + b^2 = c^2
Substituting the values we have:
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25
As we can see, the equation is balanced, which means that the 3-4-5 triangle does indeed satisfy the Pythagorean theorem. Therefore, it is a right triangle.
The 3-4-5 triangle is also a special right triangle known as a Pythagorean triple. Pythagorean triples are sets of three positive integers that satisfy the Pythagorean theorem. Other examples of Pythagorean triples include 5-12-13, 8-15-17, and 7-24-25.
In summary, a 3-4-5 triangle is a right triangle with side lengths of 3 units, 4 units, and 5 units. It satisfies the Pythagorean theorem and is a special type of right triangle called a Pythagorean triple.
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