In this page we practice understanding the visual proof of the Pythagorean Theorem using areas and right triangles.
We also practice:
- verifying the formula \(a^2 + b^2 = c^2\)
- comparing areas in different ways
- understanding why the theorem works geometrically
Example 1 – Check the Formula \((3, 4, 5)\)
Verify that \(3, 4, 5\) satisfy the theorem.
\(3^2 + 4^2 = 9 + 16 = 25\)
\(5^2 = 25\)
✅ Both sides are equal → True
Example 2 – Check \((6, 8, 10)\)
Verify that \(6, 8, 10\) satisfy the theorem.
\(6^2 + 8^2 = 36 + 64 = 100\)
\(10^2 = 100\)
✅ True
Example 3 – Check \((5, 12, 13)\)
Verify that \(5, 12, 13\) satisfy the theorem.
\(5^2 + 12^2 = 25 + 144 = 169\)
\(13^2 = 169\)
✅ True
Example 4 – Area Method
Find the area of the large square in two ways.
Side of square \(= (a + b)\)
Method 1:
Area \(= (a + b)^2\)
Method 2:
Area \(= 4(\frac12 ab) + c^2\)
👉 Both methods must give the same result
Example 5 – Why it Always Works
Explain why the theorem works.
Because the total area is the same, whether we calculate it using:
- the big square
or - triangles \(+\) small square
Practice
- More Examples (Current page)
Continue Learning
- Pythagorean Formula
- Pythagoras Theorem (a² + b² = c²) – Visual Proof 1
- Pythagoras Theorem (a² + b² = c²) – Visual Proof 2
- Pythagoras Theorem (Example)