Two polygons are similar if....
the corresponding sides are in proportion and the corresponding angles are congruent.
If two angles of one triangle are congruent
to two angles of another triangle,
then the triangles are similar.
If the three sides of one triangle are
proportional to the three sides of
then the two triangles are similar.
If two sides of one triangle are
proportional to two sides of
another triangle and the included
angles is congruent then the
triangles are similar.
Proportional parts conjecture
If two triangles are similar then the corresponding altitudes, medians and angle bisectors are proportional to the corresponding sides.
Opposite sides conjecture
A bisector of an angle in a triangle divides the opposite side into two segments whose lengths are in the same ratio as the lengths of the two sides forming the angle.
If two polygons are similar then their areas have ratio....
If two polygons are similar then their volumes have ratio...