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# Chapter 6 Notecards

TermDefinition
Ratio of a to b if a and b are two numbers or quantities and b does not = 0 then the ratio is a/b or a:b
Proportion an equation that states that two ratios are equal
Means The middles terms of a proportion
Extremes of a Proportion The first and last terms of a proportion
Cross Products Property of Proportion In a proportion the product of the extremes equals the product of he means. EX: If a/b = c/d and d does not = 0 then ad = bc
Geometric Mean two positive numbers a and b is the positive number x that satisfies a/x = x/b. so x^2 = ab and x = the square root of ab
Additional Properties of Proportions 2. Reciprocal Property: if two ratios are equal then their reciprocals are also equal. 3. If you interchange the means of proportion, then you from another true proportion. 4. In a proportion, if you add the value of each ratio's denominator to its nume
Scale Drawing is a drawing that is the same shape as the object it represents.
Scale a ratio that describes how the dimensions in the drawing are related to the actual dimensions of the object
Similar Polygons two polygons such that their corresponding angles are congruent & the lengths corresponding sides are proportional
Scale Factor the ratio of the length of two corresponding sides of two similar polygons
Perimeters of Similar Polygons Theorem if two polygons are similar then the ratio of their perimeters is equal to the ratios of their corresponding side lengths
Corresponding Lengths in Similar Polygon if two polygons are similar then the ratio of any two corresponding lengths in the polygons is equal to the scale factor of the similar polygons
AA Similarity Postulate if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar
SSS Similarity Theorem if the corresponding side lengths of two triangles are proportional, then the triangles are similar
SAS 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 if a line parallel to one side of a triangle intersects the other two sides then it divides the two sides proportionally.
Converse of the Triangle Proportionality Theorem if a line divides two sides of a triangle proportionally, then it is parallel to the third side.
Theorem 6.6 if three parallel lines intersect two transversals, then they divide the transversals proportionally
Theorem 6.7 if a ray bisects an angle of a triangle then it divides of the opposite side into segments whose lengths are proportional to the lengths of the other two sides.