Pythagorean Theorem Summary

Pythagorean Theorem Overview

• The Pythagorean Theorem relates the sides of a right triangle:

  • Formula: a^2 + b^2 = c^2

  • Where ( a ) and ( b ) are the legs, and ( c ) is the hypotenuse.

  • The theorem is fundamental in geometry and is used to find unknown lengths in right triangles.

  • It's applicable only to right triangles, which have one angle that measures exactly 90 degrees.

Right Triangle Definition

• A right triangle has one right angle (90°).

  • Legs meet at the right angle, while the hypotenuse is opposite it.

  • The legs are the two sides that form the right angle.

  • The hypotenuse is always the longest side of the right triangle.

  • The relationship holds true for all right triangles.

Applications of the Pythagorean Theorem

Example 1: Driving scenario:

• Drive 48 miles west and 36 miles south.

• Apply the theorem: 48^2 + 36^2 = c^2

• Calculation: 2304 + 1296 = 3600, thus ( c = 60 ) miles.

  • This example demonstrates how to find the straight-line distance from the starting point.

  • Useful in navigation and route planning to find the shortest distance.

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  Example 2: Diagonal of a rectangle measuring 15 inches by 8 inches:

• Calculate diagonal using: 15^2 + 8^2 = c^2.