Understanding the Pythagorean Theorem

Objective

Explore and prove the Pythagorean Theorem through various methods.

Materials

• Graph paper
• Pencils and rulers
• Right-angled triangles (drawn or physical models)
• Notebook for recording data

Instructions

1. Draw several right-angled triangles on graph paper, measuring their sides.
2. Verify the Pythagorean Theorem (\(a^2 + b^2 = c^2\)) for each triangle by calculating the squares of the sides.
3. Explore different methods of proving the theorem, such as geometric proofs or algebraic manipulation.
4. Compare the results from different methods to confirm the theorem’s validity.
5. Present your findings in a report, discussing the theorem’s importance and applications in geometry.