In this page we practice understanding the second visual proof of the Pythagorean Theorem by comparing different arrangements of the same right triangles.

We also practice:

• identifying the shapes formed inside the large square
• comparing areas
• understanding why $a^2+b^2=c^2$

Example 1 – Identify the Shapes

What shapes are formed in the first arrangement?

Answer:

• Two rectangles
• One square with side a
• One square with side b

Example 2 – Area in First Shape

Find the total area inside the big square.

Area = a² + b²

Example 3 – Area in Second Shape

Find the area inside the big square.

Area = c²

Example 4 – Compare Both Shapes

What do you notice about the areas?

Both areas are equal

So:
a² + b² = c²

Example 5 – Key Idea

Why does the theorem work?

Because we used:

• The same triangles
• The same big square

Only the arrangement changed

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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