Remember those tangrams? Well, in this lesson, we'll use those to illustrate an important property of right triangles, namely the Pythagorean Theorem.

Objective 1a

You will be able to discover, use, and prove the Pythagorean Theorem

Introductory video which reviews the area of a square (for some reason) and the parts of a right triangle. Duration_5_31

Objective 1b

In this Activity, you will use Tangrams, the enigmatic Chinese puzzle, to illustrate the Pythagorean Theorem. Duration_9_25

Objective 1c

In Investigation 1, Mr. Labelle uses Geogebra to relate the Pythagorean Theorem to the areas of squares. Duration_8_02

Objective 1d

Here, Mr. Labelle extends the previous Geogebra investigation to equilateral triangles, hexagons, and decagons. Does the Pythagorean relation still hold? Duration_7_40

Pythagorean Water Wheel

Duration_0_44

Objective 1e

In this video, we formally state the Pythagorean Theorem, see if the Pythagorean formula holds on non-right triangles, solve a traditional ladder-based problem. Duration_8_32

Objective 1f

After an SAT question, Mr. Labelle uses similar right triangles (and geometric mean) to prove the Pythagorean Theorem. Duration_7_32

Objective 1g

Because one proof is never enough, here is the ancient Chinese proof of the Pythagorean Theorem, which is oddly algebraically satisfying. Duration_7_13

Mathematical Fable

Numberphile. Duration_8_56

Objective 2a

You will be able to use Pythagorean triples to quickly find a missing side length in a right triangle

Pro-tip: If you're right triangle is a multiple of a Pythagorean triple, put down that calculator, because you won't need it. Duration_9_51

Objective 2b

In this final video, we look at a number of examples that put our Pythagorean triples to good use. Oh, and then there's another ladder problem. Duration_10_00

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

Geometry 8(B) identify and apply the relationships that exist when an altitude is drawn to the hypotenuse of a right triangle, including the geometric mean, to solve problems.