Converse of the Pythagorean theorem:

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

Use the distance formula to determine the measures of the sides of .

The distance formula is .

Find measure of QR.

              (Substitute )

                      (Subtract)

                                 (Evalute powers)

                              (Simplify)

Find measure of RS.

             (Substitute )

                         (Subtract)

                                 (Evalute powers)

                              (Simplify)

Find measure of QS.

             (Substitute )

                        (Subtract)

                               (Evalute powers)

                              (Simplify)

Check whether the mesures form a right triangle.

By the converse of the Pythagorean theorem, .

                         (Substitute , and )

                               (Evaluate powers)

                                       (Add)

Since the sum of the squares of two sides is not equals to the square of the longest side,

is not a right triangle.

is not a right triangle.