Applying the Pythagorean Theorem to rectangles (performance task)

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Applying the Pythagorean Theorem to rectangles

 

The task linked above provides an opportunity to apply the Pythagorean theorem to multiple triangles in

order to determine the length of the hypotenuse; the converse of the 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.

 

The task can be preceded or followed up by a prompt for students to look for rectangles whose

vertices lie at the intersection of the grid lines (other than the ones whose sides are contained in

the grid lines). There are many examples. It is difficult, however, to find examples where the

side lengths of the rectangle are all whole numbers as is the case for in this problem.

 

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Another perfomance task involving coordinate geometry, pythagorean theorem, and rectangles:

Is this a rectangle?

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