1. The problem asks us to determine which three sticks form a right triangle. According to the Converse of the Pythagorean Theorem, if for three side lengths $a$, $b$, and $c$ (with $c$ the longest), $a^2 + b^2 = c^2$, then the triangle is right-angled. 2. Check each combination by ordering the sides and comparing sums of squares: - Combination 1: $6$, $7$, $8$ - Longest side: $8$ - Check if $6^2 + 7^2 = 8^2$: $$6^2 + 7^2 = 36 + 49 = 85$$ $$8^2 = 64$$ $85 \neq 64$, so no. - Combination 2: $6$, $7$, $10$ - Longest side: $10$ - Check if $6^2 + 7^2 = 10^2$: $$36 + 49 = 85$$ $$10^2 = 100$$ $85 \neq 100$, so no. - Combination 3: $6$, $8$, $10$ - Longest side: $10$ - Check if $6^2 + 8^2 = 10^2$: $$36 + 64 = 100$$ $$10^2 = 100$$ $100 = 100$, so this combination forms a right triangle. - Combination 4: $7$, $8$, $10$ - Longest side: $10$ - Check if $7^2 + 8^2 = 10^2$: $$49 + 64 = 113$$ $$10^2 = 100$$ $113 \neq 100$, so no. 3. Only the combination $6$, $8$, and $10$ satisfies the converse of the Pythagorean Theorem. **Final answer:** Max should use the sticks of lengths 6, 8, and 10 inches to make a right triangle.