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.