Exercise 33 Page 553

Given the measures of all three sides of a triangle, we can determine whether it is right, acute, or obtuse by using the Converse of the Pythagorean Theorem and Pythagorean Inequalities Theorems. In each case, $c$ is the length of the longest side.

• Right: If $a^2+b^2=c^2,$ then the triangle is a right triangle.
• Acute: If $c^2<a^2+b^2,$ then the triangle is an acute triangle.
• Obtuse: If $c^2>a^2+b^2,$ then the triangle is an obtuse triangle.

Let's begin by plotting the given vertices on a coordinate plane and drawing the triangle.