Question

When three squares are joined at their vertices to form a right triangle, the combined area of the two smaller squares is the same as the area of the largest square.

Determine if each set of three squares supports this statement or does not support this statement and drag the set to the appropriate box. Note: Squares are not drawn to scale.

Supports Statement Does NOT Support Statement

Answer 1

I don’t have the pictures or the side lengths you’re sorting, so I can’t place each set for you. I can, however, tell you exactly how to decide which box each set belongs in and give a couple of quick examples.

Rule to use
- Let the three squares have side lengths a, b, c. (Sort them so c is the largest.)
- Compute a^2 + b^2 and compare it with c^2.
- If a^2 + b^2 = c^2 (within rounding tolerance), the set “Supports Statement” (this is exactly the Pythagorean condition).
- If a^2 + b^2 ≠ c^2, the set “Does NOT Support Statement.”

How to apply this in practice
1. Measure (or read) the side length of each square.
2. Square each length.
3. Add the two smaller squares’ areas and compare to the largest square’s area.

Examples
- Side lengths 3, 4, 5 → 3^2 + 4^2 = 9 + 16 = 25 = 5^2: Supports.
- Side lengths 2, 2, 3 → 4 + 4 = 8 ≠ 9: Does NOT support.

If you upload the images or give the three side lengths for each set, I’ll sort them for you.