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=SIMILAR SHAPES= __**8.1 Dilations and scale factors**__ Objectives:
 * Dilation of a segment and a point bby using scalefactor
 * Dilation of a closed plane figure

Vocabulary-
 * Dilation**- Its an example of a transformation that is not rigid
 * Scale factor**- The number //n// in the transformation
 * Contraction**- The figure is reduced in size by dilation
 * Expansion**- The figure is enlarged by a dilation
 * Center of dilation**- A point in a dilation through which every line connecting a preimage point to an image point passes

[|Dilation example]

__**8.2 Similar Polygons**__ Objectives:
 * Learn what similar polygons are
 * Use proportions and scale factors to solve problems that involve similar polygons

Vocabulary- Two polygons are similar if there ia a way of setting up a correspondence between their sides and angles so the conditions below are met:
 * Similar figures**- Figures are only similar if one is congruent to the image of the other figure by dilation
 * Proportional**- When there are two polygons and when the ratios of corresponding sides are equal
 * Proportion**- A statement of the equality of two ratios
 * Polygon Similarity Postulate**
 * Each pair of corresponding angles are congruent
 * Each pair of corresponding sides are proportional

//a, b, c//, and d are any real numbers If //a/b=c/d// and //b// and //d// not equal 0, then //ad=bc// If a/b=c/d and //a, b, c,// and //d// not equal 0, then //b/a=d/c// If a/b=c/d and //a, b, c//, and //d// not equal 0, then //a/c=b/d// If a/b=c/d and //b// and //d// not equal 0, then //a+b/b=c+d/d// [|similar polygon examples] //scroll down// Objectives:
 * __Properties of Proportions__**
 * Cross-Multiplication**
 * Reciprocal Property**
 * Exchange Property**
 * "Add-One" Property**
 * __8.3 Triangle Similarity__**
 * Learn and use the AA triangle similarity postulate and the SSS andSAS triangle similarity theorems

If a triangle has two angles that are congruent to two angles of another triangle, then therefore the triangle are similar If there are two triangle that have three sides that are proportional to the other triangle, then they are similar If there are two triangles that have two sides that are proportional to the other triangle and their included angles are congruent, then they are similar [|Theorems and examples] Objectives: A line that is parallel to one of the sides of the triangle and that divides the other two sides proportionally Parallel lines, three or more that divide two intersecting transversals proportionally
 * AA (Angle-Angle) Similarity Postulate**
 * SSS (Side-Side-Side) Similarity Theorem**
 * SAS (Side-Angle-Side) Similarity Theorem**
 * __8.4 The Side-Splitting Theorem__**
 * Learn the side-splitting theorem
 * Use the side-splitting theorem when solving problems
 * Side-Splitting Theorem**
 * Two-Transversal Proportionality Corollary**

__**8.5 Indirect Measurement and Additional Similarity Theorems**__ Objectives:
 * Measure distances indirectlt using triangle similarity
 * Learn and use similarity theorems for altitudes and medians of triangles

Corresponding altitudes have the same ratio as their corresponding sides then the trangle are similar Corresponding medians have the same ratio as their corresponding sides then the triangle are similar Corresponding angle bisectors have the same ratio as the corrsponding sides then the trangle are similar An angle bisector is what divides the opposite side into two segments that have the same rati as the other two sides of a triangle
 * Proportional Altitudes Theorem**
 * Proportional Medians Theorem**
 * Proportional Angle Bisectors Theorem**
 * Proprtional Segmetns Theorem**

Objectives: [|Ratios of similar figures] scroll down to similar figures
 * __8.6 Area and Volume Ratios__**
 * Learn and use ratios areas of similar figures
 * Learn and use ratios for volumes of similar solids
 * Relationships of cross-sectional area, weight, and height