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

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Answer 1 · 2018-04-21T18:25:19

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

$45 - 45 - 90$ $45-45-90" "$ 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 $color(blue)("no rotational symmetry.")$