45-45-90 triangle side ratios | Right triangles and trigonometry | Geometry | Khan Academy

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Showing the ratios of the sides of a 45-45-90 triangle are 1:1:sqrt(2)
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[@fsyi8395]

2 identical 45-45-90 triangles form another 45-45-90 triangle with hypotenuses as legs; since 2 identical 45-45-90 triangles form a square with legs as sides as well, area of square with hypotenuses as sides = 2 × (area of 45-45-90 triangle with hypotenuses as legs) = 2 × (area of square with legs as sides) hypotenuse^2 = 2 × leg^2 hypotenuse = √2 × leg

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[@vwlz8637]

the 30 60 90 and 45 45 90 are the triangles that are similar to the set square .

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