Chapter 10.1, Problem 34P

Open-Ended Draw a right triangle with side lengths that are whole numbers. What equation can you use to prove that you have drawn a right triangle? What theorem will you use to help make your proof?

To determine

To state the equation and the theorem required to prove that whether the triangle is a right triangle or not.

Answer to Problem 34P

The equation required to prove that it is right angle triangle is ${\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2$

The theorem used as help to prove is called Pythagoras theorem.

Explanation of Solution

Given information:

The given statement is:

“Draw a right triangle with side lengths that are whole numbers. What equation can you use to prove that you have drawn a right triangle? What theorem will you use to help make your proof?”

The right triangle with side length as whole numbers is:

  

The equation required to prove that it is right angle triangle is ${\left(hypotenuse\right)}^2={\left(base\right)}^2+{\left(height\right)}^2$

If the measurements satisfy the equation, then it is a right triangle.

The theorem used as help to prove is called Pythagoras theorem.