Similarity

Means and Extremes

Mean: b and c

Extreme: a and d

Cross Product Property (1)

If a/b = c/d, then ad = bc

Reciprocal Property (2)

If a/b = c/d, then b/a = d/c

Property of Proportions (3)

If a/b = c/d, then a/c = b/d

Property of Proportions (4)

If a/b = c/d, then (a + b)/b = (c + d)/d

Geometric Mean

Mean using proportions

Sqrt of (a x b)

Properties of Similarity

Angles are congruent and preserved

DE/AB = EF/BC = FD/CA = k (scale factor)

Perimeters of Similar Polygons Theorem

If similar then (DE + EF + FD)/(AB + BC + CA) = DE/AB = EF/BC = FD/CA

Areas of Similar Polygons Theorem

If similar then (Area of DEF/Area of ABC) = the square of each; DE/AB = EF/BC = FD/CA