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 * __CHAPTER 8__**


 * Chapter 8.1 - Dilation's and Scale factors**

Objectives:
- By using a scale factor we will construct a dilation of a point and a segment. - We also will construct a closed plane figure.

Vocabulary:
- Dilation: A translated figure that is not rigid. The dilation in a coordinate plane is found by multiplying x and y by the same number (n). ^D(x,y)=(nx,ny) - Scale Factor: The number that the points are multiplied by (n) - Center Of dilation: The center point of the dilation. - Contraction: When the figure's size is reduced by a dilation. - Expansion: When the figure's size is enlarged by the dilation.

Examples:
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 * Chpater 8.2** **- Similar Polygons**

- Similar Polygons definition. - Using proportions and scale factors to solve for similar polygons.

Vocabulary:
- Similar Figures: The two figures are congruent ONLY if one image is congruent to the other image by a dilation. - Dilation: An enlargement of an image that is a scale factor of the pre-image.

Polygon Similarity Postulate:
Two Polygons are similar if there is any corresponding angles or sides that are: - Their pairs of Corresponding angles are congruent. - Their pairs of Corresponding angles are congruent.

Properties of Proportions:
- a,b,c and d are all real numbers - When a/d=c/d and b and d DO NOT equal 0, that means ad=bc
 * Cross Multiplication Property:**

- When a/b=c/d and a,b,c and d DO NOT equal 0, that means b/a=d/c
 * Reciprocal Property:**

- When a/b=c/d and a,b,c and d DO NOT equal 0, that means a/c=b/d
 * Exchange property:**

- When a/b=c/d and b and d DO NOT equal 0, that means (a+b)/b=(c+d)/d
 * "Add One" Property:**


 * Chapter 8.3 Triangle Similarity**

Objective:
- Help understand the AA Triangle Similarity Postulate and the sss and SAS Triangle Similarity Theorems

Vocabulary:
- Similarity: Angles need to be congruent, sides need to be proportional.

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.

SSS (Side-Side-Side) Similarity Theorem:
If all three sides of a triangle are proportional to all three sides of another triangle, that means the triangles are similar.

AA ( Angle-Angle) Similarity Postulate:
If there are two angles in one triangle that happen to be congruent to two angles of another triangle, that means that they are similar.