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45°- 45°- 90° Triangle
A right triangle where the
angles are 45°, 45°, and 90°.
Try this In the figure below, drag the orange dots on each
vertex to reshape the triangle.
Note how the angles remain the same, and it maintains the same proportions between its sides.
This can be derived from Pythagoras' Theorem. This ratio will come in handy later in the study of trigonometry. In the figure above, as you drag the vertices of the triangle to resize it, the angles remain fixed and the sides remain in this ratio. Because the base angles are the same (both 45°) the two legs are equal and so the triangle is also isosceles Area of a 45-45-90 triangle
As you see from the figure on the right, two 45-45-90 triangles together make a square, so the area of one of them is half the area of the square.
As a formula
whereS is the length of either short side 
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Perimeter / Area
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