ASH Geometry Similarity
|Two polygons are similar if....||the corresponding sides are in proportion and the corresponding angles are congruent.|
|AA similarity|| If two angles of one triangle are congruent |
to two angles of another triangle,
then the triangles are similar.
|SSS similarity|| If the three sides of one triangle are |
proportional to the three sides of
then the two triangles are similar.
|SAS similarity|| 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....||(m/n)^2|
|If two polygons are similar then their volumes have ratio...||(m/n)^3|