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__8.1 Dilations and Scale Factors__
Vocab:
 * Dilation** - is an example of a transformation that is not rigid. Dilations preserve the shape of an object, but they may change its size.
 * Scale Factor** - The number by which the distance of the preimage from the center of dilation is multiplied to determine the distance of the image point from the center.
 * Center of Dilation** - In a dilation each point and its image lay on a straight line that pass through a point known as the center of diltion.
 * Contraction** - If a size of a figure is reduced by a dilation, the dilation is called a contraction.
 * Expansion** - In the size of a figure is enlarged by a dilation, the dilation is called an expansion.



__8.2 Similar Polygons__
Vocab:
 * Similar Figures** - Two figures are similar if and only if one is congruent to the image of the other by a dilation.
 * Proportional** - When the rations of corresponding sides of two polygons are equal the sides are said to be proportional.
 * Proportion -** A statement of the equality of two ratios is called a proportion.
 * Polygon Similarity Postulate -** Two pilygons are similar if and only if --the following conditions are met
 * each pair of corresponding angles is congruent.
 * each pair of corresponding sides is proportional.

Properties of Proportions
If a/b=c/d and b and d0, then ad is equal to bc If a/b and c/d and a, b, c, and d0, then b/a is equal to d/c If a/b=c/d and a, b, c and d0, then a/c is equal to b/d If a/b=c/d and b and d0, then a+b/b is equal to c+d/d
 * Cross-multiplication**
 * Reciprocal Property**
 * Exchange Porperty**
 * "Add-One" Property**

= =

= = CLICK HERE FOR SOLUTION.
 * EXAMPLE**

__8.3 Triangle Similarity__
Vocab:
 * AA (angle-angle) Similarity Postulate -** If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
 * SSS (Side-Side-Side) Similarity Theorem** - If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are similar.
 * SAS(Side-Angle-Side) Similarity Theorem** - If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.



__8.4 The Side Splitting Theorem__
Vocab:
 * Side-Splitting Theorem** - A line parallel to one side of a triangle divides the other two sides proportionally.
 * Two-Transversal Proportionality Corollary** - Three or more parallel lines divide two intersecting tranversals proportionally.

CLICK HERE FOR THE SOLUTION
 * EXAMPLE.**

__8.5 Indirect Measurement and Additional Similarity Theorems__
If two triangles are similar, then their corresponding altitudes have the same ratio as their corresponding sides. If two triangles are similar, then the corresponding medians have the same ratio as their corresponding sides. If two triangles are similar, then their corresponding angle bisectors have the same ratio as the corresponding sides. An angle bisector of a triangle divides the opposite side into two segments that have the same ratio as the other two sides. CLICK HERE FOR SOLUTION
 * Proportional Altitudes Theorem** :
 * Proportional Medians Theorem**:
 * Proportional Angle Bisectors Theorem**:
 * Proportional Segments Theorem**:
 * EXAMPLE.**

__8.6 - Area and Volume Ratios__


The Golden Ratio.

Other Math Sites To Help Understand Chapter 8. http://library.thinkquest.org/20991/geo/spoly.html -- similar polygons http://argyll.epsb.ca/jreed/math9/strand3/3303.htm -- dilation http://math.usask.ca/emr/tri.html -- triangle similarity http://www.mathwarehouse.com/geometry/similar/triangles/side-splitter-theorem.php -- For some examples to try and figure out using the theorems in chapter 8 ^