Notes
right-angled triangle

Right-Angled Triangle

A right-angled triangle is a triangle in which one of the angles is a right angle.

The side opposite the right-angle is known as the hypotenuse of the triangle.

Calculating Lengths

In a right-angled triangle the lengths of the sides are related via Pythagoras Theorem: with side lengths $a$ , $b$ , and $c$ where $c$ is the hypotenuse then the following identity holds:

a^2 + b^2 = c^2

Division into Isosceles Triangles

A useful fact about right-angled triangles is that they can be divided into two isosceles triangles. Mark a point at the midpoint of the hypotenuse and join it to the vertex where the right-angle is located. This splits the triangle into two isosceles triangles.

One way to see this is to complete the triangle to a rectangle. The hypotenuse becomes a diagonal of the rectangle. The other diagonal crosses this hypotenuse at its midpoint, and symmetry shows that the four half-diagonals are all the same length. In the rectangle there are four isosceles triangles and two of them coincide with the original right-angled triangle.

category: shapes

category: triangles

Revised on August 13, 2021 18:28:26 by Andrew Stacey

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