Pythagorean Theorem

Pythagorean Theorem

Student’s Name




The Pythagorean Theorem describes the lengths of the sides of a right triangle in a practical way and is still widely used today. The theorem states that for any right triangle, the sum of the squares of the non-hypotenuse sides is equal to the square of the hypotenuse (Padovan, 2002). In other words, for a right triangle with perpendicular sides of length a and b and hypotenuse of length c, a2 + b2 = c2. The Pythagorean Theorem is one of the fundamental pillars of basic geometry, having countless practical applications such as finding the distance between two points on a coordinate plane.

During their workday, architects and carpenters’ find themselves using a special type of right triangle where the lengths of the triad are always integers. In correlation, the Pythagorean Theorem is a useful and necessary tool in measuring surface areas and volumes of various geometric shapes; and calculating maxima and minima of perimeters, or surface areas and volumes of various geometric shapes. Often, when builders want to lay the foundation for the corners of a building, one of the methods they use is based on the Pythagorean Theorem. The carpenters and architectures use tape measures to calculate corner right angle (Eli , 2007)

Builders use this special triangle when they don’t have a carpenter’s square. Builders often need to construct a square corner. The Pythagorean Theorem tells us that if a corner is square, then the Sides of a triangle built on that corner will satisfy the formula a2 + b2 = c2, but we can also prove that the converse of the theorem is true. If the sides of a triangle satisfy the formula a2 + b2 = c2, then the triangle is a right triangle, with a square to prove converse concept. The online Pythagorean Theorem Calculator is used to calculate the length of third side of right triangle based on the other two sides using the Pythagorean Theorem. This animated PowerPoint presentation uses shearing and the invariance of the area of triangles with congruent bases and heights to show a step-by-step geometric proof of the Pythagorean Theorem.


Eli, M. (2007). The Pythagorean Theorem: A 4,000-year history. (p. 166). New York: Princeton University Press

Padovan, R. (2002). Proportion: Science, philosophy, architecture. (pp. 116-125). New York: Taylor & Francis,..