Basic Elements of a Right Triangle

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In a right triangle, different elements can be distinguished, referring to its sides and angles.

Drawing the elements of a right triangle

  • Legs (or cathetus): are the sides of the triangle that together form the right angle.
  • Hypotenuse: is the largest side of the triangle opposite the right angle.
  • Right angle: is a 90° angle formed by the two legs.
  • Acute angles: the other two angles of the triangle (α and β) are less than 90°.

Download this calculator to get the results of the formulas on this page. Choose the initial data and enter it in the upper left box. For results, press ENTER.

Triangle-total.rar         or   Triangle-total.exe      

Note. Courtesy of the author: José María Pareja Marcano. Chemist. Seville, Spain.

Relationship between Legs and Hypotenuse

Pythagorean Theorem

Right triangle

The Pythagorean theorem, also known as Pythagoras’s theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle (2 legs and hypotenuse). This theorem can be written as the following equation:

Pythagorean theorem formula

Geometric Mean Theorem

Drawing the right triangle for the height theorem

The Geometric mean theorem (or Altitude-on-Hypotenuse Theorem) relates the height (h) of the triangle and the legs of two triangles similar to the main ABC, by plotting the height h over the hypotenuse, stating that in every right triangle, the height (h) relative to the hypotenuse is the geometric mean of the two projections of the legs on the hypotenuse (n and m).

Height theorem formula

Leg Rule

The leg rule is a theorem that relates the segments projected by the legs on the hypotenuse with the legs they touch.

Drawing of the right triangle for the leg theorem

In every right triangle, a leg (a or b) is the geometric mean between the hypotenuse (c) and the projection of that leg on it (n or m).

Leg theorem formula

AUTHOR: Bernat Requena Serra

YEAR: 2020


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