Students will learn how to prove what is sometimes referred to as, the inverse Pythagorean theorem, \(a^{-2} + b^{-2} = h^{-2},\) where \(h\) is the height of the triangle.

Pythagorean Theorem and Its Inverse (My Favorite Proofs) by blackpenredpen

Next, give your students these challenges:

- Remainders of Two by MAA
- Opening Patterns by NRICH
- Street Sequences by NRICH

Conclude by leading this investigation:

Lazy Toad Puzzles (counting, symmetry)

by MathPickle