1. Daniel Cohen & Jacob Singer

2. 8.1 = Dilations and Scale Factors 8.2 = Similar Polygons 8.3 = Triangle Similarity

3. Dilations and Scale Factors Dilation = A transformation that is not rigid. Preserves the shape of an object, but the size may vary. (Example: Your eyes will dilate to adjust to brightness). Dilations can be found on a coordinate plane by multiplying the x and y coordinates of a point by the same number n. D(x, y) = (nx, ny) The number n called a scale factor. Types of Dilations: Contraction = The sixe of a figure is reduced by the dilation. ( l n l < 1 ) Expansion = The size of the figure is enlarged by the dilation. ( l n l > 1 )

4. Similar Polygons 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 ratios of corresponding sides of two polygons are equal Proportion = The statement of the equality of two ratios. Polygon Similarity Postulate = Two polygons can only be similar if each pair of corresponding angles are congruent, and each pair of corresponding sides are proportional. (Hint – The letters of the vertices of the polygons must be written in corresponding order.)

5. When working with similar figures, it is often helpful to know the following: Properties of Proportions: Cross-Multiplication: If a / b = c / d, then ad = bc (d ≠ 0) Reciprocal: If a / b = c / d, then b / a = d / c (a, b, c, and d ≠ 0) Exchange: If a / b = c / d, then a / c = b / d (a, b, c, and d ≠ 0) “Add One”: If a / b = c / d, then (a + b) / b = (c + d) / d (b and d ≠ 0)

6. Triangle Similarity Here are some helpful shortcuts for determining triangle similarity! Yayyyy! AA (Angle – Angle) Similarity Postulate: If two angles of a triangle are congruent to two angles of another triangle, then the triangles are similar. SSS (Side – Side – Side) Similarity Theorem: If 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.

7. Click Here to go to Polygon Similarity land! Click Here for fun proportion information!

8. Click Here to go to Fun Triangle Similarity World! Dilations and Scale Factors Quiz Polygon Similarity Quiz