# ASH Geometry Similarity

## 8 terms

### 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
another triangle,
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.

(m/n)^2

(m/n)^3