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8.1 Dilations and Scale Facters
[|This link is for the butterflys] In this chapter, you would need to use some old parts of the book. Dilation - transforming something to a different angle. Scale Facter - It's a number n, that is being multiplies by each coordinate. Center of Dilation - A straight line and it's pre-image line passes through this point. Contraction - Something like a drawing of two things, but one is reduse. Expansion - If you have notice that you have grown from a yung age to your hight? Maybe the different hight from a young kid to you? That will be Expansion.

8.2 Similar Polygons
Similar Figures - Two same things are simlir if they are congruent to the image of the other by a dilation. Like a small baby to the mom. Polyhon Similarity Postulate - 1)Each pair has a (or more) correponding angles congruent. Later sections needs one ore more angles congruent. 2) Each pair of corrspondiong sides proortional. Some need to be equal. Next few lines are from Properties of Proportions. Cross-Multiplication Property - If a/b=c/d with b and d not equal to 0, then ad =bc. Reciprocal Property - If a/b=c/d with a, b, c, and d are not equal to 0, then b/a=d/c. Exchange Property - If a/b=c/d with a, b, c, and d are not equal to 0, then a/c=b/d. "Add-One" Property - If a/b=c/d with b and d not equal to 0, than a+b/b=c+d/d.

8.3 Triangle Simlarity
AA (Angle-Angle) Similarity Postulate - If two angles of one triangle are congruent to two sangles of another triangle, then the triangles are similar. SSS (Side-Side-Side) Similarity Theorem - If the three sides of one triangle are proportional to the three sides of another triangle, the the triangles are similarity. SAS (Side-Angle-Side) Similarity Theorm - If two sides of one triangle are proportional to the two sides of another triangle and their included angles are congruent, then the triangles are similar.

8.4 The Side-Splitting Theorem
Side-Splitting Theorem - A line parallel to one side of the triangle divides the other two sides proportially. Two-Transversal Proportionality Corollary - Three or more parallel lines divide two intersection transversals proportionally.

8.5 Indirection Measurement and Additional Similarity Theorems
Proportional Altitudes Theorem - If two triangles are similar, then thier corresponding altitudes have the same ratio as the corresponding sides. Proportional medians Theorem - If two triangles are silmilar, then thier corresponding medians have the same as thir corresponding sides. Proportional Angle Bisectors Theorem - If two triangles are similar, then their corresponding angle bisectors have the same rato as the corresponding sides. Proportional Segments Theorem - An angle bisdtor 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
The formulas are sumetimes like chapter 7. You may need to use them. Bigger number on tap and keem the the same for all of them and don't change after you start the problem, but sometimes the bigger number could be on the bottom too. The following is always used for sides. side of square A/ side of square B = ?/? side of triangle A/side of triangle B = ?/? side of rectangle A/side of rectangle B = ?/? radius of circle A/radius of circle B = ?/? the fallowing can be used for any above problems. area of circle A/area of circle B = ?/? This is the fallowing can be used for volumes. edges of cube A/edges of cube B = ?/? edge of prism A/edge of prism B = ?/? radus of sphere A/radus of sphere B = ?/? radius of cylinder A/ radis of cylinder B = ?/? This is for volume for all of the volume ?'s. volume of cube A/volume of cube B = ?/? Ex. The square A has a side length of 19 m and square B has a side length of 29 m. Whch number will be on top? Wich on the bottom?..........................It's 19/29 if you got it right. Then grabe somthig heathy if you got it right!! But what is the smallest fraction you can get? ..................................................... It's 19/29, if you got that right and did you homework, then go and play!!!