Similar triangles calculator
Calculator shows relation between two similar triangles. Enter angles and lengths and see live preview of your triangles.

Beta version#

This online calculator is currently under heavy development. It may or it may NOT work correctly.
You CAN try to use it. You CAN even get the proper results.
However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.
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Calculations data - angles and sides of your triangles#

The first triangle (primary triangle)
The first side of primary triangle (a)
The second side of primary triangle (b)
The third side of primary triangle (c)
The second triangle (the mirror image of first one)
The first side of secondary triangle (a')
The second side of secondary triangle (b')
The third side of secondary triangle (c')
Angles (the same in both triangles)
Angle opposite to a side (α)
Angle opposite to b side (β)
Angle opposite to c side (γ)
Similarity scale

Drawing - how your triangles look like#

a=2 cmb=2 cmc=2 cmγβαa'=1 cmb'=1 cmc'=1 cmγβα

Some facts#

  • If the sides of two triangles can be paired with the same ratio, we say that such triangles are similar. This property can be written as follows:
    aa=bb=cc=s\dfrac{a}{a'} = \dfrac{b}{b'} = \dfrac{c}{c'} = s
    • a, b, c - sides lengths of the first triangle,
    • a', b', c' - sides lengths of the second triangle,
    • s - proportionality factor called the similarity scale.
  • The angle values in similar triangles are identical:
    {α=αβ=βγ=γ\begin{cases}\alpha = \alpha'\\ \beta = \beta'\\ \gamma = \gamma'\end{cases}
  • To determine if the given two triangles are similar, it is sufficient to show that one of the following triangles similarity criteria is met:
    • SSS similarity (side-side-side) - the length ratios of the respective pairs of sides are equal,
    • SAS similarity (side-angle-side) - the ratios of the length of two pairs of sides equal and the measure of the angles between these sides are equal,
    • AAA similarity (angle-angle-angle) - the measures of appropriate angles are kept (the equality of two pairs of angles is enough here, because the sum of angles measures in triangle is equal to 180°).
  • Operations that keep the similarity property are:
    • rotation - rotation of the whole shape around selected point,
    • translation - translate of the whole shape by selected vector,
    • scale up/down - elongation or shortening of all sides using the same factor.

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