# Proof PT

Can you easily prove Pythagoras theorem using Euclidean theorems? If so, do it.

Result

#### Solution:

$a^2 = c_a \cdot c \ \\ b^2 = c_b \cdot c \ \\ a^2 + b^2 = c_a \cdot c + c_b \cdot c \ \\ a^2 + b^2 = c\cdot (c_a + c_b ) \ \\ a^2 + b^2 = c\cdot c \ \\ a^2 + b^2 = c^2$

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