Date modified: Tue 2023-08-15 . 02:56 PM
Date created: Sat 2023-10-07 . 09:02 PM
# Pythagorean theorem. Pythagorean theorem states: Given a right triangle with sides $a,b,c$, where side $c$ is opposing a right angle, then we have $$ a^{2}+ b^{2}=c^{2} $$ ![[summer program 2023/puzzles-and-problems/---files/pythagorean-theorem 2023-08-15 11.08.51.excalidraw.svg]] %%[[summer program 2023/puzzles-and-problems/---files/pythagorean-theorem 2023-08-15 11.08.51.excalidraw.md|🖋 Edit in Excalidraw]], and the [[summer program 2023/puzzles-and-problems/---files/pythagorean-theorem 2023-08-15 11.08.51.excalidraw.dark.svg|dark exported image]]%% By why is this true? Start with four copies of this same right triangle, and arrange them so we have **a square inside a square**. Then calculate areas in two different ways and prove Pythagorean theorem. Hint: The arrangement that might be helpful looks something like this: ![[summer program 2023/puzzles-and-problems/---files/pythagorean-theorem 2023-08-15 14.52.05.excalidraw.svg]] %%[[summer program 2023/puzzles-and-problems/---files/pythagorean-theorem 2023-08-15 14.52.05.excalidraw.md|🖋 Edit in Excalidraw]], and the [[summer program 2023/puzzles-and-problems/---files/pythagorean-theorem 2023-08-15 14.52.05.excalidraw.dark.svg|dark exported image]]%% (Label in all the corresponding sides...)