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.

3² + 4² = 9 + 16 = 25
5² = 25

✅ Both sides are equal → True

Example 2 – Check (6, 8, 10)

Verify that 6, 8, 10 satisfy the theorem.

6² + 8² = 36 + 64 = 100
10² = 100

✅ True

Example 3 – Check (5, 12, 13)

Verify that 5, 12, 13 satisfy the theorem.

5² + 12² = 25 + 144 = 169
13² = 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(½ab) + c²

👉 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

• Take the Quiz

Continue Learning

1. Pythagorean Formula
2. Pythagoras Theorem (a² + b² = c²) – Visual Proof 1
3. Pythagoras Theorem (a² + b² = c²) – Visual Proof 2
4. Pythagoras Theorem (Example)

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