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Chapter 8.1 Notes Ratio – if a and b are 2 quantities that are measured in the same units, then the ratio of a to b is a/b. (i.e. a ratio is a fraction) Proportion – is an equation that equates 2 ratios Means a = c Extremes b d Properties of Proportions If a = c , then ad = bc (Cross Product Prop.) b d If a = c , then b = d (Reciprocal Prop.) b d a c Chapter 8.2 Notes Properties of Proportions If a = c , then a = b b d c (Rotation) d If a = c , then a+ b = c + d b d b d (Add the denominator to the numerator) Geometric Mean – of two positive numbers a and b is the positive number x such that a = x when solved x = √a * b x b Example: Find the geometric mean of 4 and 9. answer: 6 Chapter 8.3 Notes Similar Polygons – when you have 2 polygons that have all corresponding ∠’s are ≌ and all corresponding sides are in the same proportion then they are similar (~) A X B C Y Z Thm – if 2 polygons are ~, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths Scale Factor – if 2 polygons are ~, then the ratio of the lengths of 2 corresponding side is called the scale factor. We usually write scale factors like this a:b Chapter 8.4 Notes Similar Triangles 1) AA (angle-angle similarity postulate) If 2 ∠’s of one triangle are ≌ to 2 ∠’s of another triangle, then the 2 ∠’s are ~ Chapter 8.5 Notes Similar Triangles 1) AA (angle-angle similarity postulate) 2) SSS (side-side-side similarity postulate) 3) SAS (side-angle-side similarity postulate) Chapter 8.6 Notes Triangle Proportionality Thm If then Converse of the Triangle Proportionality Thm If then Thm If then Thm If then Chapter 8.7 Notes Dilations 1) reduction – which means it is getting smaller A A’ 2) enlargement – which means it is getting larger A A’