kiscjo6pareke6


 * 8.1** **Dilations and Scale Factors**



[|dilation]-a transformation in which each point p has an image point p' such that a line conecting the two points passes through point O,know as the center of dialation,and OP' = k x OP, where k is the scale factor of the dialation. Example (1,0) and ( 5,3) n = 2 (1x2,0x2) and (5x2,3x2) (2,0) and (10,6) new points [|Pi picture] 8.2 **Similar Polygons** [|similar figures] - two figures are similar if and only if one is congruent to the image of the oth by a dilation cross multiplication property reciprocal property exchange property "add-one" property example two building are being compared one has dimensions of 25 x 12 and 18 x X. find X. X 12cross multiply and divide 18x12=216 / 25=8.6418 = 25 over 18 = 25
 * scale factor**- in a transformation the number by which the distance ofthe preimage from the center of dilation is multiplied to determine the distance of the image point from the center.
 * center of dilation**- point in the dilation through which every line connecting a preimage point to an image point pases
 * contraction**- when the size of the figure is reduced by a dilation
 * expansion**- when the size of the figure is enlarged by a dilation
 * polygon similarity postulate**- two polygons are similar if and only if there is a way of setting up a correspondence between their sides and angles such that the following are met.
 * Each pair of corresponding angles is congruent
 * Each pair of corrseponding sides is proportional
 * properties of proportions- let a,b,c and d be any real number
 * properties of proportions- let a,b,c and d be any real number
 * if a/b=c/d and b and d /0, then ad = bc
 * if a/b c/d and a,b,c, and d /= 0, then b/a=d/c
 * if a/b c/d and a,b,c, and d /= 0, then a/c = b/d
 * if a/b c/d and b and d /= 0, then a + b / b = c + d / d

8.3 Tirangle Similarity
(Angle-Angle) Similarity postulate- If two angles of one triangle are congruent to two angles of another triangle, then the triangles are. example:
 * SSS ( SIde-Side-Side) Similarity Theorem- If the three sides of one triangle are proportional to the three sides of another triangle, then the triangles are.
 * SAS (Side-Angle-Side) Similarity Theorem- If two sides of one triangle are proportional to two sides of another and their agles are congruent, then the triangles are.



8.4 The Side-Splitting Theorem
If you look in the middle of the spider web there is triangles.
 * Side-Spilitting Theorem- A line parallel to one side of the triangle rdivides the other tw osides proportionally.
 * Two-Transversal Proportionality Corollary-Three or more parallel lines divide two intersecting transversals
 * [[image:http://farm1.static.flickr.com/33/46989574_dec3d1f857_m.jpg width="240" height="180" link="http://www.flickr.com/photos/vidoman/46989574/"]]



8.5 Indirect measurement and additional Similarity Theorems
Proportional Segment Theorem- An angle bisector of a triangle divides the opposite side into two segments that have the same ratio as the other two sides.
 * Proportional Altutudes Theorem- If two [|triangles] are similar, then their corresponding altitudes have the same ratio as their corresponding sides.
 * Proportional Medians Theorem- If two triangles are similar, then their corresponding medians have the same ratio as their [|corresponding sides].
 * Proportional Angles Bisectors Therem- If two triangles are similar, then their corresponding angle bisectors have the same ratio as the corresponding sides.




 * 8.6 Area and Volume Ratio**

How to find the ratio for the shapes.


 * Two squares[[image:square_prob_KP.JPG align="right"]]**

Big square of side by the small square side. Big is 3 and if the small is 1.

side of square A 3 = --- side of square B 1

area of square A ? = --- area of square B ?

Two triangles[[image:triangle_kp.JPG align="right"]]
Big triangle is 2 and the small triangle is 1. side of triangle A 2 = side of triangle B 1

area of triangle A ? =

area of triangle B ?

Two rectangles
The big rectangles is 3 and the small is 2. side of rectangle A 3 =

side of rectangle B 2

area of rectagle A ? = --- area of rectagle B ?

Two circles
Find the radius of a circle and divide it by two. If the big one is 8 for the radius and the other is 6 for the radius. radius of circle A 4 = --- radius of circle B 3

area of circle A ? = --- area of circle B ?