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Pythagorean theorem

a² + b² = c² in a right triangle, and where it comes from.

In a right triangle the square built on the hypotenuse has the same area as the two squares on the legs put together. That single fact gives the distance formula, the equation of a circle, and half of trigonometry.

Shembulli i punuar: hypotenuse of 3 and 4

Geometry · Pythagorean-Theorem

Hypotenuse of 3 and 4

3,\ 4

Hap pas hapi

  1. c^2 = a^2 + b^2 = 3^2 + 4^2 = 25

    Pythagoras: in a right triangle the square on the hypotenuse equals the sum of the squares on the legs.

  2. c = \sqrt{25} = 5

    Take the square root.

Zbulo përgjigjen
c = 5

Symbols used here

\sqrt{x},\ \sqrt[n]{x}
square root, n-th root
The non-negative number whose square (n-th power) is x.
\pi
pi
Ratio of a circle's circumference to its diameter, 3.14159…
\theta
theta
The usual name for an angle.
^\circ
degrees
1/360 of a full turn. 180° = π radians.
\sin,\ \cos,\ \tan
sine, cosine, tangent
Ratios of sides in a right triangle; coordinates on the unit circle.
\angle ABC,\ \triangle ABC
angle, triangle
The angle at B between BA and BC; the triangle with those vertices.
\parallel,\ \perp,\ \cong,\ \sim
parallel, perpendicular, congruent, similar
Never meet; meet at 90°; identical shape and size; same shape.

How to: Pythagorean theorem

  1. Pythagoras: in a right triangle the square on the hypotenuse equals the sum of the squares on the legs.
  2. Take the square root.

Questions people ask

Why does every triangle have angles adding to 180°?

Draw a line through one vertex parallel to the opposite side: the two alternate angles equal the other two angles of the triangle, and the three angles at the vertex lie on a straight line. That is Euclid's proof, and it is why the fact holds only on a flat plane.

When do I use the law of sines versus the law of cosines?

Cosines when you know three sides, or two sides and the angle between them. Sines when you know an angle and the side opposite it, plus one more piece.

What is the difference between area and perimeter?

Perimeter is the length of the boundary (one dimension, measured in metres); area is the amount of surface inside (two dimensions, square metres). Doubling every side doubles the perimeter but quadruples the area.

Provo timen.

Më shumë në Geometry

TrianglesCirclesPolygonsSolidsCoordinate geometryEuclid's axioms and the structure of proofCongruent and similar trianglesCircle theoremsTransformations: translation, rotation, reflection, dilationSolid geometry: prisms, pyramids, spheres