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" "# 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.")#