treani3

CHAPTER 8:

8.1

OBJECTIVES:

Construct a dilation of a segment and a point by using a scale factor.

Construct a dilation of a closed plane figure.

TERMS:

dilation: a tranformation in which every point P has an image of point P'such as a line connecting the two points passes through a point O known as the center of dilation and OP' where k is the scale factor of the dilation.

scale factor: in a tranformation the number by which the distance of the preimage from the center of dilation is multiplied to determine the distance of the image point from center.

center of dilation: the point at the holes line up to produce some type of dilation

contraction: a dilation in which the preimage is reduced in size

expansion: a dilation in which the preimage is enlarged in size

BLUE BOXES:

NONE FOR THIS SECTION

8.2

OBJECTIVES:

Define similar polygons.

Use Properties of Proportions and scale factors to solve problems involving similar polygons.

TERMS:

similiar: two figures are similar if and onl if one is congruent to the image of the other by dilation.

BLUE BOXES:

definition of similiar figures: two figures are similiar if and only if one is congruent to the image of the other by a dilation.

polygon similiarity postulate: two polygons are similiar if and only if there is a way of setting up a correspondence between their sides and angles such that the following conditions are met: Their pairs of Corresponding angles are congruent. Their pairs of Corresponding angles are congruent.

properties of porportions: let a, b, c, and d equal any real number cross-multiplication property: When a/d=c/d and b and d do not equal 0, that means ad=bc reciprocal property: When a/b=c/d and a,b,c and d do not equal 0, that means a/c=b/d exange property: When a/b=c/d and a,b,c and d do not equal 0, that means a/c=b/d "add one" property: When a/b=c/d and b and d DO NOT equal 0, that means (a+b)/b=(c+d)/d

8.3

OBJECTIVES:

Develop the AA Triangle Similarity Postulate and the SSS and SAS Triangle Similarity Theorems.

TERMS:

NONE FOR THIS SECTION

BLUE BOXES:

aa (angle angle) similiarity theorem: If there are two angles in one triangle that happen to be congruent to two angles of another triangle, that means that they are similar.

sss (side side side) similiarity theorem: If all three sides of a triangle are proportional to all three sides of another triangle, that means the triangles are similar.

sas (side angle side) similiarity 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.

8.4

OBJECTIVES:

Develop and prove the Side-Splitting Theorem

Use the Side-Splitting Theorem to solve problems

TERMS:

NONE FOR THIS SECTION

BLUE BOXES:

side-splitting theorem: A line parallel to one side of the triangle divides the other two sides proportionally.

two-transaversal porportionality corollary: Three or more parallel lines divide two intersecting transversals proportionally.

8.5

OBJECTIVES:

Use triangle simpilarity to measure distances indirectly.

Develope and use similiarity theorems for altitudes and medians of triangles.

TERMS:

NONE FOR THIS SECTION

BLUE BOXES:

Proportional Altitudes 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 Angle Bisectors Theorem: If two triangles are similar, then their corresponding angle bisectors have the same ratio as the corresponding sides

Proportional Segments Theorem: An angle bisector of a triangle divides the opposite side into two segments that have the same ratio as the other two sides.

8.6

OBJECTIVES:

Develop and use ratios for areas of similar figures.

Develop and use ratios for volumes of similar solids.

Explore relationships between cross-sectional area, weight, and height.

TERMS:

NONE FOR THIS SECTION

BLUE BOXES:

NONE FOR THIS SECTION