3:4:5 Triangles

The 3:4:5 triangle is one of the most common triangles used in mathematics. It is also known as the Pythagorean Triple or the Pythagorean Quadrilateral. The 3:4:5 triangle consists of three equal sides and five equal angles (180°). The first four sides are called the hypotenuse and they form a right angled rectangle with each other and their perpendicular neighbours.

For example, if the hypotenuse is the right angle between two adjacent sides, then it forms a right angled rectangle with its neighbour. If there are no other neighbours, then it forms a straight line segment joining them all.

If the hypotenuse is any number from 1 to 6, then it forms a square with its opposite side and its four neighbours. If the opposite side is less than or equal to the hypotenuse, then it forms a right angled quadrilateral with its neighbours.

If the opposite side is greater than or equal to the hypotenuse, then it forms a parallelogram with its neighbours.

In general, when you multiply two numbers together and add them together, you get another number which is half of both of those original numbers.

In the diagram above, the hypotenuse is at point A. Point B is at point C and points D, E and F are all on the same side of the triangle. The diagram shows that if you add up all these numbers, you get another number which equals 2 + 3 = 6. This is called the sum of squares or simply squared.

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