# Geometry: Understanding the Pythagoras Theorem

Years ago, a mathematician namely Pythagoras stated a theorem on right angles triangles. Hence the theorem is named as Pythagoras theorem. Pythagoras theorem states that “In a right angled triangle, the square of length of the hypotenuse (the longest side) is the sum of the squares of the other two sides.
By Pythagoras theorem,
c

^{2}= a^{2}+b^{2}where**is the hypotenuse and***c***,***a***are the legs of the right angle triangle. This means that, if we frame the squares along all the three sides of a right angled triangle then the area of square along hypotenuse is equal to the areas of the other two squares put together.***b***Example:**Here 5^{2}= 3^{2}+ 4^{2}25 = 9+16 25=25. So, Pythagoras theorem is used to determine whether the given triangle is right-angled. Since here we got 25=25 using the statement of Pythagoras theorem, we can say that the triangle with lengths 3,4 and 5 is right-angled. Also, Pythagoras theorem is used to determine the length of an unknown side of a right angled triangle.**Example:**By Pythagoras theorem, a^{2}+ 4^{2}= 52 a^{2}+ 16 = 25 a^{2}= 25-16=9 a = √9=3 In the same way, Pythagoras theorem is used to obtain the formula for the diagonal of a square. Since all the angles in square are right angles, Pythagoras theorem can be applicable for the triangle which is inside the square. So, diagonal^{2}= a^{2}+a^{2}=2a^{2}So,**the diagonal of square = √2 a**Still need help with Mathematics? Please read more about our Mathematics tutoring services. SchoolTutoring Academy is the premier educational services company for K-12 and college students. We offer tutoring programs for students in K-12, AP classes, and college. To learn more about how we help parents and students in Newman visit: Tutoring in Newman.