15 points The side lengths of four triangles are shown in the table. Select all the triangles that are right triangles.

9514 1404 393

  I, III

Step-by-step explanation:

You know from your study of the Pythagorean theorem that a triangle with sides 3, 4, and 5 will be a right triangle. Any scaled version of this triangle will also be a right triangle, so it is helpful to learn to recognize when scaled values of these numbers are used.

  I -- the scale factor for a 3-4-5 right triangle is 2/10

  II -- no isosceles right triangle has integer side lengths. (not a right triangle)

  III -- the scale factor for a 3-4-5 right triangle is 1/13

  IV -- the lengths do not form a triangle

Triangles I and III are right triangles.

Additional comment

The sides of an isosceles right triangle have the ratios 1 : 1 : √2. The square root of 2 is irrational. No scaled version of this triangle can have rational side lengths.

0 is its x and y coordinate