Task# Sizing up Squares

Illustrative MathematicsVaries

The goal of this task is for students to check that the Pythagorean Theorem holds for two specific examples. Although the work of this task does not provide a proof for the full Pythagorean Theorem, it prepares students for the area calculations they will need to make as well as the difficulty of showing that a quadrilateral in the plane is a square. For the right isosceles triangle, students can find the area of the three squares built on the sides of the triangle and verify that that the sum of the areas of the smaller squares is equal to the area of the largest square. One special feature of this right triangle is that students can produce a good argument for why the quadrilateral with the hypotenuse as one edge is a square.