| A | B |
|---|
| 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 measures of the corresponding sides of two triangles are proportional, then the triangles are similar. |
| SAS Similarity | If the measures of two sides of a triangle are proportional to the measures of two corresponding sides of another triangle and the included angles are congruent, then the triangles are similar. |
| Theorem 7-3 | Similarity of triangles is reflexive, symmetric, and transitive. |
| Triangle Proportionality | If a line is parallel to one side of a triangle the other two sides in two distinct points, then it separates these sides into segments of proportional lengths. |
| Theorem 7-6 | A segment whose endpoints are the midpoints of two sides of a triangle is parallel to the third side of the triangle and its length is one-half the length of the third side. |
| Corollary 7-1 | if three or more parallel lines intersect two transversals, then they cut off the transversals proportionally. |
| Corollary 7-2 | : If three or more parallel lines cut off congruent segments on one transversal, then they cut off congruent segments on every transversal. |
| Proportional Perimeters | If two triangles are similar, them the perimeters are proportional to the measures of corresponding sides. |
| Theorem 7-8 | If two triangles are similar, then the measures of the corresponding altitudes are proportional to the measures of the corresponding sides. |
| Theorem 7-9 | If two triangles are similar, then the measures of the corresponding angle bisectors are proportional to the measures of the corresponding sides. |
| Theorem 7-10 | If two triangles are similar, then the measures of the corresponding medians ate proportional to the measures of the corresponding sides. |
| Angle Bisector Theorem | An angle bisector in a triangle separated the opposite side into segments that have the same ratio as the other two sides. |
