1.8 Right Triangle Trigonometry
The Pythagorean Theorem
Pacing:This lesson should take one class period
Goal: This lesson introduces the Pythagorean Theorem. It is arguably one of the most important theorems in
mathematics, allowing for a multitude of uses, including the Law of Cosines.
Visualization!Here is a second proof of Pythagorean’s Theorem that students can do in class.
a. Reproduce the following diagram for each student.
b. Students cut the red square and the blue square from the triangle.
c. Cut along the lines within the blue square. Students should have four pieces.
d. Students will fit these four puzzle pieces onto the yellow triangle, proving that the combined area of the two
smaller squares equal the area of the largest square. Hence,a^2 +b^2 =c^2Illustration_to_Euclid’s_proof_of_the_Pythagorean_theorem.svg
Additional Examples:
a. A rectangular park measures 500 m by 650 m. How much shorter is the path diagonally than walking around
the outside edge?
b. Television sets are described according to its diagonal length. A 42[U+0080][U+009D]TV means the diago-
nal of the screen is 42[U+0080][U+009D]long. Suppose the TV below is 36[U+0080][U+009D]tall with a
47 [U+0080][U+009D]diagonal. How wide is the TV?1.8. Right Triangle Trigonometry