# Pythagorean Theorem: Applications to Different Triangle Types

This page expands on the Pythagorean Theorem by applying it to different types of triangles: right triangles, obtuse triangles, and acute triangles. Understanding these applications is crucial for **classifying triangles using Pythagorean Theorem**.

## Right Triangles

For right triangles, the Pythagorean Theorem holds true in its original form:

c² = a² + b²

**Example**: In a right triangle with c = 5 and b = 4, we can find a:
5² = a² + 4²
25 = a² + 16
a² = 9
a = 3

## Obtuse Triangles

For obtuse triangles, the square of the longest side is greater than the sum of squares of the other two sides:

c² > a² + b²

**Example**: In an obtuse triangle with c = 6 and b = 4, we can verify:
6² > 3² + 4²
36 > 9 + 16
36 > 25

## Acute Triangles

For acute triangles, the square of the longest side is less than the sum of squares of the other two sides:

c² < a² + b²

**Example**: In an acute triangle with c = 4 and b = 3, we can verify:
4² < 3² + 3²
16 < 9 + 9
16 < 18

**Highlight**: The relationship between the squares of the sides in different triangle types helps in **classifying triangles using Pythagorean Theorem**.

These applications of the Pythagorean Theorem demonstrate its versatility in geometry and provide a foundation for solving more complex **Pythagorean Theorem problems**. Students can use these principles to tackle various **Pythagorean Theorem examples with answers** and improve their problem-solving skills in geometry.