Workers at the Pythagorean Construction Company are building a new house. They need to make sure that proper right triangles are formed to ensure that a safe house is built. What statement should the builders use to ensure that right triangles are formed? If the sum of the two shorter sides equals the longest side, then the triangle is a right triangle. If the sum of the squares of the two longer sides equals the square of the shortest side, then the triangle is a right triangle. If the sum of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle. If the difference of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle.

The Pythagoras theorem states that if a triangle is right-angled (90 degrees), then the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The Pythagoras theorem equation is expressed as, c2 = a2 + b2, where 'c' = hypotenuse of the right triangle and 'a' and 'b' are the other two legs. Hence, any triangle with one angle equal to 90 degrees produces a Pythagoras triangle and the Pythagoras equation can be applied in the triangle.

example:

The hypotenuse of a right-angled triangle is 16 units and one of the sides of the triangle is 8 units. Find the measure of the third side using the Pythagoras theorem formula.

Given : Hypotenuse = 16 units

Let us consider the given side of a triangle as the perpendicular height = 8 units

On substituting the given dimensions to the Pythagoras theorem formula

Hypotenuse2 = Base2 + Height2

162 = B2 + 82

B2 = 256 - 64

B = √192 = 13.856 units

So, Using the definition of Pythagoras theorem

the statement would be

If the sum of the squares of the two shorter sides equals the square of the longest side, then the triangle is a right triangle.

Learn more about pythagoras theorem here:

brainly.com/question/343682

#SPJ2