Similarity

Ratio

Comparison of 2 values in the form of a fraction

Extended Ratio

Comparison of 3 or more values

Proportions

When 2 ratios are =, Can use cross product property to solve

Simular Polygons

Same shape, different size

Corresp. angles are congruent

Corresp. sides are **PROPORTIONAL**

Corresp. lengths in Simular Polygons

If 2 polygons are \~, then the ratio of any 2 corresp. length in the polygon is = to the scale factor of the similar polygons

Theorem Perimeters of Simular Polygons

If 2 polygons are \~, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths

Theorem Areas of Simular Polygons

If 2 polygons are \~, then the ratio of their area is = to the squares of the ratios of their corresp. side lengths

AA Similarity Theorem

If 2\~ of one triangle are congruent to two angles of another triangle, then the triangles are simular.

SSS Similarity Theorem

If the corresp. side lengths of triangles are proportional, then the triangles are simular

SAS Similarity Theorem

If the angle of one triangle is congruent to the angle of the other triangle, and the included sides are proportional, then the triangles are similar.

Triangle Proportionality Theorem

If a line is ll to one side of a triangle intersects the other two sides, then it divides the two sides proportionally

3 ll Lines Theorem

If 3 ll lines intersect 2 transversals, then they divide the transversal proportionally

Triangle Angle Bisector

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