## Proportions and Similarity Ch 6

##### Created by:

rustyparker  on January 30, 2012

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# Proportions and Similarity Ch 6

 RatioComparison of two numbers such as [a:b]
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#### English

Ratio Comparison of two numbers such as [a:b]
Proportion An equation that states 2 ratios are equal.
AA Similarity If 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are similar.
SSS Similarity If the measures of corresponding sides of 2 triangles are proportional, then the triangles are similar
SAS Similarity If the measures of 2 sides of a triangle are proportional to the measures of 2 corresponding sides of another triangle, and their included angles are congruent, then the triangles are similar.
Scale Factor The common ratio of the lengths of two corresponding sides of similar polygons
Side Proportionality If two triangles are similar, the corresponding sides are in proportion.
Triangle Proportionality Theorem A line drawn parallel to a side of a triangle, intersecting the two remaining sides of the triangle, divides those sides proportionally.
Converse of the Triangle Proportionality Theorem If a line divides two sides of a triangle proportionally, that line is parallel to the third side of the triangle.
Midsegment Theorem The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.
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)
three parallel lines intersect two transversals If three parallel lines intersect two transversals, then they divide the transversals proportionally
Triangle Angle-Bisector Theorem If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides.
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
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

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