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# Math 8.1-8.7

### Chapter 8.1-8.7 (whole chapter) vocab

ratio of a to b the quotient a/b if a and b are two quantities that are measured in the same units. can also be written a : b
proportion an equation that equates two ratios. a and d are called exetremes. c and b are called means.
Cross Product Property the product of the exetremes equals the product of the means.if a/b=c/d then ad=bc
Reciprocal Property If two ratios are equal, then their reciprocals are also equal.If a/b=c/d then b/a=d/c
geometric mean for two positive numbers a and b, the positive number x such that:a/x=x/b or x = the radical of axb
similar polygons two polygons such that their correspdoning angles are congruent and the lengths of the corresponding sides are proportional.
scale factor the ratio of the lengths of two corresponding sides of two similar polygons
If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths
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 lengths of the corresponding sides of two triangles are proportional then the triangles are similar
side-angle-side 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 the 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
if three parallel lines intersect two transversals then they divide the transversals proportionally
if a ray bisects an angle of a triangle then it divides the opposite sdie into segments whose lengths are proportional to the lengths of the other two sides
Dilation a type of transformation with center C and scale factor k that maps every point P in the plane to a point P' so the following properties are true:1. If P is not the center point C then the image point P' lies on ray CP. the scale factor k is a positive
number such that k=CP'/CP and k is not equal to 12. If P is the center point C then P = P'
Enlargement k is between 0 and 1
reduction k is larger than 1
Created by: jumpthemoon