Proportion
An equation that states that two ratios are equal
Means
In a proportion, the denominator of the first equation and the numerator of the second equation
Extremes
In a proportion, the numerator of the first equation and the denominator of the second equation
Geometric Mean
A positive number that satisfies the proportion a/x= x/b; x = sqrt(ab)
Scale Factor
The common ratio of the lengths of two corresponding sides of similar polygons
Perimeters of Similar Polygons
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding lengths (same scale factor)
AA
Angle-Angle similarity postulate: If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar
SSS
Side-Side-Side similarity theorem: If the corresponding side lengths of two triangles are proportional, then the triangles are similar
SAS
Side-Angle-Side 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 and Converse
A line is parallel to one side of a triangle IFF it intersects the other two sides proportionally
Transversal Similarity Theorem
If three parallel lines intersect two transversals, then they divide the transversals proportionally
Angle Bisector Similarity 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
Ratio
The comparison of two numbers using division
Cross Product Property
In a proportion, the product of the extremes equals the product of the means: if a/b = c/d (and b and d both not 0) then ad = bc
Mean Proportional
Another name for Geometric Mean (x = sqrt(ab))
Reciprocal Property
Given a proportion, the reciprocals of the ratios are equal: if a/b = c/d then b/a = d/c
Interchange Means
Given a proportion, if you interchange the means (or the extremes!), then you form another true proportion: if a/b = c/d then a/c = b/d
Add Denominator
Given a proportion, if you add the value of the denominator to the numerator, then you form a true proportion: if a/b = c/d then (a+b)/b = (c + d)/d
Similar Polygons
Two polygons in which the corresponding angles are congruent and corresponding side lengths are proportional; similar polygons have the same shape, but not necessarily the same size; angles are congruent and sides are in proportion (have a common scale fa
Extended ratios
Ratios that compare more than 2 values; example: ratios of the angles of a triangle are 1:2:3 - find the measures of the angles (answer: 30, 60, 90 degrees)