Proportions and Similarity Ch 6
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Created by:
rustyparker on January 30, 2012
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17 terms
Math / Symbols | 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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