# 9th: Chapter 7: Ratio Proportion, and Similarity

## 14 terms · Definitions, Postulates, Theorems, Corollaries, etc.

### ratio (of one number to another)

quotient when the first number is divided by the second

### proportion

equation stating that two ratios are equal

### extremes

first and last terms in a proportion

### means

middle terms in a proportion

### Property of Proportion (1)- a/b = c/d is equivalent to

ad = bc (cross multiplucation)
a/c = b/d (simplifying across the equation)
b/a = d/c (reciprocals)
a+b/b = c+d/d

### Property of Proportion (2)- if a/b = c/d = e/f = ... then

a+c+e+.../b+d+f+... = a/b

### similar polygons

polygons whose vertices can be paired that:
1) corr. angles congruent
2) corr. sides are in proportion (lengths have the same ratio)

### scale factor (of similarity)

ratio of the lengths of two corr. sides of two similar polygons

### AA~

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

### SAS~

If an angle of one triangle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar.

### SSS~

If the sides of two triangles are in proportion, 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 those sides proportionally.

proportionally

### Triangle Angle-Bisector Theorem

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