# Chapter 8: Similarity - Theorems & Postulates

## 8 terms

### Perimeters of Similar Polygons Theorem

If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.

### Angle-Angle (AA) Similarity Postulate

If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

### Side-Side-Side (SSS) Similarity Theorem

If the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.

### Side-Angle-Side (SAS) Similarity Theorem

If an angle of one triangle is congruent to an angle of a second triangle and the lengths of the sides including these angles are proportional, then the triangles are similar.

### Triangle Proportionality Theorem

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

### Converse of the Triangle Proportionality Theorem

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

### Parallel Lines Proportionality Theorem

If three parallel lines intersect two transversals, then they divide the transversals proportionally.

### Angle Bisector Proportionality Theorem

If a ray bisects an angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the other two sides.