Summary of "TEOREMA DE PITÁGORAS"

Pythagorean theorem (video)

Definition: A right triangle has one 90° angle. The two sides that meet at the right angle are the legs; the side opposite the right angle (the longest side) is the hypotenuse.
Theorem (for right triangles):

If a and b are the legs and c is the hypotenuse, then a^2 + b^2 = c^2.
Geometric interpretation: The area of the square built on the hypotenuse equals the sum of the areas of the squares built on the two legs (visual/area-proof idea).
Practical usage — two main problem types:
- Given both legs, find the hypotenuse.
- Given the hypotenuse and one leg, find the other leg.
Tip: Always first identify the right angle so you know which sides are legs and which is the hypotenuse. Letters a, b, c are just labels — what matters is which side is opposite the right angle.

Steps:

Example (legs 3 cm and 4 cm):

Steps:

Example 1:

Example 2:

Interpretation: ladder length = hypotenuse, wall height = one leg, distance from wall = the other leg.
Identify which lengths are given and which is unknown, then use the appropriate method above.

Example:

A 10 m ladder leans with its foot 8 m from the wall.
c = 10, one leg = 8 → other leg = sqrt(10^2 − 8^2) = sqrt(100 − 64) = sqrt(36) = 6 m

The theorem only applies to right triangles.
Always identify the right angle first to label legs and the hypotenuse correctly.
Process summary:
- To find c: add squares of legs, then take the square root.
- To find a leg: subtract square of the known leg from square of hypotenuse, then take the square root.
Letters (a, b, c) are labels — adapt them to whichever sides are legs and hypotenuse in the problem.