Question

Discuss with your friends that in what way similarity of triangles is different from similarity of other polygons?

Answer 1

When we say two shapes are similar, it means that one shape is a scaled version of the other. They could be oriented or tilted differently though.

For polygons(including triangles), similarity means that the corresponding angles are same. The converse is also true, that is, if corresponding angles of two polygons are equal, then the two polygons are similar.

If two polygons are similar then it also means that the lengths of their corresponding sides are scaled by common factor.

The converse, however, is not true for polygons in general. If all the sides are scaled by a common factor, the two polygons are not necessarily similar. For example, a rhombus and a square are not similar although their sides are equal.

For triangle though,it is true. If it is known that there is a common factor between the lengths of sides of two triangles then the two triangles are similar.