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 photo of the other).
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Try thisDrag any kind of orange period at either triangle"s vertex. Both triangle will readjust shape and remain similar to each other.
Triangles are comparable if they have the very same shape, however not have to the very same size. You can think that it as "zooming in" or out making the triangle bigger or smaller, yet keeping its an easy shape.In the figure above, together you drag any type of vertex ~ above triangle PQR, the various other triangle changes to be the same shape, but half the size.In official notation we can write
which is review as "Triangle PQR is comparable to triangle P"Q"R" ".The letter v a little vertical dash after the such as P" is read as "P prime".
Properties of comparable Triangles
Corresponding angles space congruent (same measure)So in the figure above, the angle P=P", Q=Q", and also R=R".
Corresponding sides space all in the very same proportionAbove, PQ is twice the length of P"Q". Therefore, the other pairs of sides are also in the proportion. PR is double P"R" and also RQ is twice R"Q". Formally, in two comparable triangles PQR and also P"Q"R" :
One triangle deserve to be rotated, yet as long as they are the very same shape, the triangles room still similar. In the figure below, the triangle PQR is similar to P"Q"R" even though the latter is rotatedclockwise 90°.
In this specific example, the triangles are the exact same size, for this reason they are likewise congruent.
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