Question

What are the basic properties of a 45-45-90 triangle?

Answer 1

Consider the properties of the sides, the angles and the symmetry.

Explanation:

`45-45-90" "` refers to the angles of the triangle.

The `color(blue)("sum of the angles is " 180°)`

There are `color(blue)("two equal angles")`, so this is an isosceles triangle.

It therefore also has `color(blue)(" two equal sides.")`

The third angle is `90°`. It is a `color(blue)("right-angled triangle")` therefore Pythagoras' Theorem can be used.

The `color(blue)("sides are in the ratio " 1 :1: sqrt2)`

It has `color(blue)("one line of symmetry")` - the perpendicular bisector of the base (the hypotenuse) passes through the vertex, (the `90°` angle).

It has `color(blue)("no rotational symmetry.")`