Chapter 6

Ratio- ratio m to n is m:n

Proportion- when 2 ratios are equal

a/b = c/d:

• a and d are the extreme

• b and c are the mean

Geometric mean- proportions where the means are equal. Always has a negative and positive answer

*When comparing changes to a proportion make sure that the cross products are equal

Polygons are similar if

• corresponding angles are congruent and

• corresponding side lengths are proportional

*All congruent polygons are similar but not all similar polygons are congruent

Statement of proportionality- side/ corresponding side = side 2/ corresponding side 2 = side 3/ corresponding side 3

Scale factor- ratio of the corresponding sides

Proving triangle similarities

1 AA~ post- when 2 angles of a triangle are congruent to two angles of another triangle

2 SSS~thm- when all corresponding sides of a triangle are proportional

3 SAS~thm- when the corresponding middle angles are congruent and the corresponding sides are proportional

triangle proportionality thm/ side splitter thm- when a || side of a triangle intersects the other two sides, then it divides it proportionally

*If a line divides two sides of a triangle proportionally then it’s || to the third side

Angle bisector thm- if there’s a triangle and there’s an angle bisector in one of the angles, then the segment divided will have the same ratio as the non divided sides