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Math: Chapter 6

TermDefinition
Ratio a/b a:b a to b
Proportion An equation that states two ratios are equal. a/b=c/d
Mean In a/b=c/d b and c are the means.
Extreme In a/b=c/d a and d are the extremes.
Geometric Mean The positive number that satisfies a/x=x/b so x
Ratio a/b a:b a to b
Proportion A equation that states tow ratios are equal. a/b=c/d
Extreme In a/b=c/d A and D are the extremes.
Mean In a/b=c/d B and C are the means.
Geometric Means The positive number x that satisfies a/x=x/b so x•x=ab and x=√ab.
Cross Product Property The Product of the extremes equals the products of the means. ad=bc
Scale Drawing A drawing that is the same shape as the object it represents.
Scale The ratio that describes how the dimensions in a scale drawing are related to the original dimensions of the real object.
Reciprocal Property If two ratios are equal their reciprocals are also equal. a/b=c/d then b/a=d/c
Means Property If you interchange the means of a proportion then you form another true proportion.
Denominator Property If you add the value of each ratios denominator to its numerator, then you form another true proportion.
SImilar Polygons If corresponding sides are proportional and corresponding angles are congruent then figures are similar. Represented by ~
Scale Factor The ratio of two corresponding lengths of two similar polygons.
Perimeters of Similar Polygons Theorem If two polygons are similar the ratios of the perimeters is equal to the scale factor.
Angle Angle Similarity Postulate If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Side Side Side Similarity Theorem If the corresponding side lengths of two triangle are proportional then the triangles are similar.
Side Angle SIde Similarity Theorem If an angle of one triangle is congruent to the corresponding 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 then it divides those sides proportionally.
Converse of the Triangle Proportionality Theorem If a line divides two side of a triangle proportionally then it is parallel to the third side.
Theorem 6.6 I If three parallel intersect two transversals then they divide the transversals proportionally.
Theorem 6.7 If a ray bisects an angle of a triangle then it divides the opposite side into segments that are proportional to the length of the other two sides.
Dialation A transformation that stretches or shrinks a figure to create a similar figure.
Reduction If the scale factor of a dilation is greater than zero but less than one the dilation is a reduction.
Enlargement If the scale factor of a dilation is greater than one it is an enlargement.
Created by: 18blake_jessica