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The Pythagorean Theorem

The Hook

The legend itself.

What is it?

In a right triangle, the square of the hypotenuse equals the sum of the squares of the legs (a² + b² = c²).

Time Travel (History)

Used by rope-stretchers in Egypt to create perfect 90-degree corners for pyramids using a 3-4-5 rope.

Cheat Code

Legs are short. Hypotenuse is long. Square them, add them, root them.

Practice This Now!

The Field Guide

In Plain English: If you know two sides of a right angle (L-shape), you can calculate the diagonal connecting them. It connects Geometry (shapes) with Algebra (equations).

In The Real World: Navigation. If you fly 300 miles East and 400 miles North, this theorem tells you exactly how far you are from the airport.

How To Do It

  1. Identify the Legs (a, b) touching the right angle.
  2. Identify the Hypotenuse (c) across from the right angle.
  3. Formula: a² + b² = c².
  4. Solve for the missing letter (Subtract if finding a leg, Add if finding hypotenuse).

Booby Trap!

Forgetting the Square Root! If a² + b² = 25, the answer is not 25. It is 5.

Real World Challenge
"A ladder is 5m long. The base is 3m from the wall. How high does it reach?"
The Logic: We have leg (3) and hypotenuse (5). 3² + b² = 5². 9 + b² = 25. b² = 16. Height is 4m.

Training Drills

The 3-4-5
3² + 4² = 5² 9 + 16 = 25
Most common example.