In two similar triangles, their perimeters and corresponding sides, medians and altitudes will all be in the same ratio.

In two similar triangles:

- The perimeters of the two triangles are in the same ratio as the sides.
- The corresponding sides, medians and altitudes will all be in this same ratio.

This is illustrated by the two similar triangles in the figure above. Here are shown one of the medians of each triangle. As you resize the triangle PQR, you can see that the ratio of the sides is always equal to the ratio of the medians. In the same way, the perimeters will be in the same ratio and the altitudes will also be in the same ratio.

There are ten items altogether that are in the same ratio (perimeter, three medians, three altitudes, three sides). To avoid cluttering up the diagram above, the ratios of just one side and one median are shown, but the idea applies to all ten items.

Remember that a triangle has three sides, three altitudes and three medians.
Be sure to compare the corresponding part in each triangle.
For example in the figure below the two altitudes are *corresponding*
altitudes because they are drawn form the same vertex in each triangle, and so the
ratio of their lengths is valid.

Be especially vigilant where one triangle is rotated and / or mirror-image of the other. To see this, in the figure at the top drag the point P down below Q. The triangle will be rotated 180° but the triangles are still similar and the ratios still hold.

See also Similar Triangles - ratios of areas

- Similar Triangles defined
- Testing for similarity
- Three sides in proportion (SSS)
- Three angles the same (AAA)
- Two sides in proportion,

included angle equal (SAS) - Similar triangles - ratio of parts
- Similar triangles - ratio of areas

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