Lesson #2 - Augsburg College

Geometry: A Shapely Approach to Math
Since we know it is a square, each of its sides must be 5, since 5 × 5 = 25. Thus, if we look at one of the
triangles highlighted in blue earlier, we see that one of its sides is 3, the other 4, and we have just shown that the
third side must have length 5!
Part 2: Other Right Triangles
We begin with the right triangle below, with sides a, b, and c. We give these sides names with letters since
we don’t know how long they are. Thus, to prove the Pythagorean Theorem, we need to show that a 2 + b 2 = c 2 . A
proof is outlined below.
For this proof, we can use a similar illustration as before to show that, for all right triangles the sum of the
squares of the two legs (a 2 + b 2 ) equals the square of the hypotenuse (c 2 ).
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