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=//__**SIMILAR SHAPES**__//=

__8.1 Dilations and Scale Factors__
//Objectives:// 1.)Construct a dilation of a segment and a point by using a scale factor. 2.) Construct a dilation of a closed plane figure.

//Vocab:// __Dilation__- A transformation in which every point P has and image point P' such that a line connecting the two points passes through a point O, known as the //center of dilation,// and OP' = k•OP, where k is the //scale factor// of the dilation.

__Scale factor__- In a transformation, 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__- The point in a dilation through which every line connecting a preimage point to an image point passes.

__Contraction__- A dilation in which the preimage is reduced in size.

__Expansion__- A dilation in which the preimage is enlarged in size.

__8.2 Similar polygons__
//Objectives:// 1.) Define //similar polygons//. 2.) Use Properties of Proportions scale factors to solve problems involving similar polygons.

//Vocab:// proportional- proportion-

//Similar Figures:// Two figures are **similar** if and only if one is congruent to the image of the other by a dilation.

//Polygon Similarity Postulate// Two polygons are similar if and only if there is a way of setting up a correspondence between their sides and angles such that the following conditions are met:
 * Each pair of corresponding angles is congruent.
 * Each pair of corresponding sides is proportional.

//Properties of Proportions// __Cross Multiplication Property__ If a/b=c/d and b and do not equal 0, then ad=bc __Reciprocal Property__ If a/b=c/d and a, b, c, and d do not equal 0, then b/a=d/c

__Exhange Property__ If a/b=c/d and a, b, c, and d do not equal 0, then a/c=b/d

__"Add-One" Property__ If a/b=c/d and b and d do not equal, then a+b/b=c+d/d

__8.3 Triangle Similarity__
//Objectives:// 1.) Develop the AA Triangle Similarity Postulate and the SSS and SAS Triangle Similarity Theorems.

//Angle Angle Similarity Postulate// If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.

//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.

//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__
//Objectives:// 1.) Develop and prove the Side-Splitting Theorem. 2.) Use the Side-Splitting Theorem to solve problems.

//Side- Splitting Theorem// A line parallel to one side fo the triangle divides the other two sides proportionally.

//Two- Transversal Proportionality Corollary// Three or more parallel lines divide two intersecting transversals proprotionally.

__8.5 Indirect Measurment and Additional Similarity Theorems__
====== //Objectives:// 1.) Use triangle similarity to measure distances indirectly. 2.) Decelop and use similarity theorems for altitudes and medians of triangles.

//Proportional Altitudes Theorem// If two triangles are similar, then their corresponding altitudes have the same ratio as their corresponding sides.

//Proportional Medians Theorem// If two triangles are similar, then their corresponding medians have the same ratio as their corresponding sides.

//Proportional Angle Bisectors Theorem// If two triangles are similar, then their corresponding angle bisectors have the same ratio as the corresponding sides.

//Proportional Segments Theorem// An angle bisector of a triangle divides the opposite side into two segments that have the same ratio as the other two sides.

__8.6 Area and Volume Ratios__
//Objectives:// 1.) Develop and use ratios for areas of similar figures. 2.) Develop and use ratios for volumes of similar solids. 3.)Explore relationships between cross-sectional area, weight, and height.

__Links__:

[|Dilations]

[|Triangle Similarity Quiz]

[|Similar Polygons]