The Pythagorean Theorem is just one of those theorems that's just as useful backwards as it is forwards, as the Egyptian Rope Stretchers well knew.

In the Geogebra investigation below, drag point D to see what happens to the Pythagorean formula when your triangle is just not right. To get started, collapse the purple menu bar and then zoom to fit your screen.

Objective 1a

You will be able to investigate and use the Converse of the Pythagorean Theorem

In this initial video, we examine the Pythagorean Theorem as an if-then conditional and state its converse. Then we discuss how we can use string (from a kite or a sweater) to investigate whether or not that converse is actually true. Duration: 7_10

Objective 1b

Using some old kite string, a marker, a ruler, and my mom's good fabric scissors, I channel the mathematical spirits of the ancient Egyptians to investigate the Converse of the Pythagorean Theorem. Duration: 3_46

Objective 1c

Turns out, those Egyptians knew what they were doing. The Converse of the Pythagorean Theorem is, in fact, an excellent way to see if you have yourself a right triangle. Examples 2, 3, and 4 demonstrate exactly that. Duration: 11_41

Objective 2a

You will be able to classify triangles using the Pythagorean Formula

Using a Geogebra demonstration, we see just what happens when the square of the length of the longest side of our triangle is not equal to the sum of the squares of the other two sides. Duration: 7_55

Objective 2b

In Examples 5 and 6, we pair the Triangle Inequality Theorem with our two new theorems about acute and obtuse triangles in at least one problem that will put our peerless algebra skills to the test. Duration: 22_04

Geometry 5(D) verify the Triangle Inequality theorem using constructions and apply the theorem to solve problems.

Geometry 6(D) verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems