Chapter 8 Flashcards
Proportion
Equation stating that two ratios are equal
Ratio
Comparison of two numbers using division
Cross product property
If a/b=c/d, then ad=bc
Reciprocal property
If a/b=c/d, then b/a=d/c
Interchange means property
If a/b=c/d, then a/c=b/d
Unnamed property
A/b=c/d iff a+b/b=c+d/d
Geometric mean
The geometric mean of two numbers a + b is the positive number X such that
A/x=x/b
Similar polygons
Two polygons are similar if their corresponding angles are congruent and the lengths of the corresponding sides are proportional
Scale factor
The common ratio between the corresponding lengths of similar polygons
Theorem 8.1
If two polygons are similar then the ratio of their perimeters is equal to the ratio of their corresponding sides
Angle angle similarity postulate
If two angles of one triangle are congruent to two angles of a second triangle than the triangles are similar
SSS similarity theorem
If the sides of one triangle are proportional to the corresponding sides of another triangle then the triangles are similar
SAS similarity theorem
If two sides of one triangle are proportional to two sides of a second triangle and the included angles are congruent 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
Triangle proportionality converse
If a line divides two sides of a triangle proportionally then it is parallel to the third side
