neumje5

=CHAPTER 8=



8.1 vocabulary Dilation- and example of a transformation that is not rigid. They keep the shape of the object, but may change the size. Scale Factor- the number,n, of the tranformation. Center Of Dilation- in a dilation where each point and it's image are on a straid line that passes through a poing called the center of dilation. (point of origin on a graph) Contraction- when the size of a figure is __reduced__ by a dilation. Expansion- when the size of a figure is __enlarged__ by a dilation.

Example of Dilation (look at both eyes)

8.2 vocabulary Similar Figures- two figures are similar if and only if one is congruent by dilation of the other image. Polygon Similarity Postulate- Two polygons are similar if and only if there is a way of setting up a corrspondnce between their sides and angles; -every pair of corresponding angles are congruent -every pair of corresponding sides are proportional if a/b=c/d and b a d [/=], then ad=bc if a/b=c/d and a, b, c and d [/=], then b/a=d/c if a/b=c/d and a, b, c and d[/=], then a+b**/**b=c+d/d if a/b=c/d and b and d [/=], then a+b/b = c+d/d
 * __PROPERTIES OF PROPORTIONS__** (let a, b, c and d be any real numbers)
 * Cross Multiplication Property-**
 * Reciprocol Property-**
 * Exchange Property-**
 * "Add One" Property-**

8.3 vocabulary AA (Angle-Angle) Similarity Postulate- -If two angles of one triangle are conguent to two angles of another triange, then the triangles are similar. SSS (Side-Side-Side) Similarity Theorem- -The Two triangles are similar if three sides of one triangle are proportional to the three sides of another triangle. SAS (Side-Angle-Side) Similarity Theorem- -The two triangles are similar if two sides of one tiangle are proportional to two sides of another triangle and their included angles are congruent. SAS Similarity Theorem

8.4 vocabulary Side Splitting Theorem- a line parallel to one side of a triangle divides the other two sides proportionally. Two Transversal Proportionality Corollary- three of more parallel lines divide two intersecting transversals proportionally.

8.5

vocabulary Proportional Altitudes Theorem- If two triangles are similar, then their corresponding altitudes have the same ratio as their corrsponding sides. Proportional Medians Theorem- If two triangles are similiar, then their corresponding medians ahve the same ratio as their corresponding sides.