Task# A rectangle in the coordinate plane

Illustrative MathematicsVaries

This task provides an opportunity to apply the Pythagorean theorem to multiple triangles in order to determine the length of the hypotenuse. Pythagorean theorem is also required in order to conclude that certain angles are right angles. In parts (a) and (b), the Pythagorean theorem can be used to find the different segment lengths because the lines of the coordinate grid make right angles where they meet. These coordinates are essential in order to measure the distance between points joined by horizontal or vertical lines. Part (c) of this problem uses the converse of the Pythagorean theorem: if the sum of the squares of two side lengths of a triangle is equal to the square of the third side length, then the triangle must be a right triangle.