Pythagorean theorem: a2 + b2 = c2. b. NOTE: The “c” side is always the side opposite the right angle. Side “c” is called the hypotenuse.
Pythagorean theorem: If a triangle is a right triangle (has one right angle), then a2+b2=c2. Conversely, if a2+b2=c2 in a triangle with c as the longest side, then a triangle is a right triangle.
The formula (a2 + b2) is written as a2 + b2 expressed > = (a +b)2 -2ab.
Pythagorean theorem reversed
The converse of Pythagorean theorem states that if the square of the third side of a triangle is equal to the sum of its two shorter sides, then it must be a right angle triangle. In other words, the inverse of the Pythagorean theorem is the same Pythagorean theorem but turned around.
c is equal to the hypotenuse and a and b are the shorter sides (you can choose which you want a or b to be)
The formula a2 + b2 + c2 is one of the important algebraic identities. It is read as a square plus b square plus c square. Its formula a2 + b2 + c2 is expressed as a2 + b2< /sup> + c2 = (a + b + c)2 – 2(ab + bc + ca).
Definition of the Pythagorean theorem
: a theorem of geometry: the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.< /p>
This theorem applies to this right triangle – the sum of the squares of the lengths of both legs is equal to the square of the length of the hypotenuse. And indeed it is true for all right triangles. The Pythagorean theorem can also be represented in terms of area.
Different ways to find the third side of a triangle
For a right triangle, use the Pythagorean Theorem. For an isosceles triangle, use the area formula for an isosceles triangle. If you know some angles and other side lengths, use the law of cosines or the law of sines.