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 proportion

Above, 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" :

Rotation

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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Reflection

One triangle deserve to be a mirror picture of the other, but as lengthy as they space the exact same shape, the triangles are still similar. It have the right to be reflect in any direction, increase down, left, right.In the number below, triangle PQR is a mirror photo of P"Q"R", however is tho considered comparable to it.
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How to tell if triangles space similar

Any triangle is characterized by six steps (three sides, three angles). But you don"t must know all of them to show that 2 triangles room similar. Various teams of 3 will do. Triangles are similar if:

Similar Triangles can have mutual parts

Two triangles deserve to be similar, also if castle share some elements. In the figure below,the bigger triangle PQR is similar to the smaller one STR. S and also T are the midpoints of PR and QR respectively. Lock share the peak R and component of the sides PR and also QR. Lock are similar on the basis of AAA,since the corresponding angles in every triangle space the same.
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