Definition: Triangles are similar if they have the same shape, but can be different sizes.
(They are still similar even if one is rotated, or one is a mirror image of the other).
Try this Drag any orange dot at either triangle's vertex. Both triangles will change shape and remain similar to each other.
Triangles are similar if they have the same shape, but not necessarily the same size. You can think of it as "zooming in" or out making the triangle bigger or smaller, but keeping its basic shape. In the figure above, as you drag any vertex on triangle PQR, the other triangle changes to be the same shape, but half the size. In formal notation we can write
which is read as "Triangle PQR is similar to triangle P'Q'R' ". The letter with a small vertical dash after it such as P' is read as "P prime".
Properties of Similar TrianglesOne triangle can be rotated, but as long as they are the same shape, the triangles are still similar. In the figure below, the triangle PQR is similar to P'Q'R' even though the latter is rotated clockwise 90°.
In this particular example, the triangles are the same size, so they are also congruent.
Reflection One triangle can be a mirror image of the other, but as long as they are the same shape, the triangles are still similar. It can be reflected in any direction, up down, left, right. In the figure below, triangle PQR is a mirror image of P'Q'R', but is still considered similar to it. How to tell if triangles are similar Any triangle is defined by six measures (three sides, three angles). But you don't need to know all of them to show that two triangles are similar. Various groups of three will do. Triangles are similar if:(C) 2011 Copyright Math Open Reference.
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