Honors Math 2 Name: Pythagorean Theorem Date: The Pythagorean Theorem states: Given a right triangle with hypotenuse of length C and legs of length A and B, then 𝑨𝟐 + 𝑩𝟐 = 𝑪𝟐 There are many ways to proof the Pythagorean Theorem. Proof 1: Start with any right triangle From the triangle above, you can construct the two figures below. Use these figures to prove the Pythagorean Theorem. (Hint: Think about area) Proof 2 (Credited to Bhaskara Acharya 1114-­‐1185) Start with any right triangle From the triangle above, you can construct the figure below. Use this figure to prove the Pythagorean Theorem. The Pythagorean Theorem relates the side lengths of right triangles. What is the relationship between the lengths of the sides in an acute or obtuse triangle? Given: Triangle 1 Triangle 2 C
C
A
A
B
B
𝐴! + 𝐵! = 𝐶! ! 𝐴! + 𝐵! < 𝐶! ! Prove: Triangle 2 is obtuse. (Hint: Think about the Hinge Theorem) Now prove if 𝐴! + 𝐵! > 𝐶 ! , then the triangle is acute.