7.4 - 7.6

7.4: SSS and SAS Similarity

SSS Similarity Postulate:

   If the corresponding sides of two triangles are proportionate, then the two triangles are similar.

SAS Similarity Postulate:

   If an angle of one triangle and the length of the sides that include these angles are proportionate, then the triangles are similar.

Nothing was difficult in this section

7.5: Proportions and Similar Triangles

Proportionality:

   If GP:PH = JQ:QK then GH and JK are divided proportionally 

Triangle Proportionality Theorem:

   If a line parallel to one side of a triangle intersects 

the other sides, then it divides the two sides proportionally.

Converse of the Triangle Proportionality Theorem:

   If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Midsegment Theorem:

   The segment connecting the midpoints of two sides of a triangle is

parallel to the third side and it is half as long.

Nothing in this section challenged me

7.6: Dilations

Dilation: 

   A dilation is a transformation with center C and scale factor K that maps each point P to an image point P(prime) so that P(prime) lies on CP and CP(prime) = K x CP.

   A dilation maps a figure onto a similar figure called the image.

   In a dilation, every image is similar to the original figure.

Types of Dilations:

   If the image is smaller then the original, the dilation is a reduction.

   If the image is larger than the original, the dilation is an enlargement.

Scale Factor:

   The scale factor of a dilation is the ratio of CP(prime) to CP.

   

The most challenging thing in this section was the scale factor. I learned that, once I found that CP(prime) is always over CP, the scale factor wasn't hard to figure out.

Overall:

   Overall, I thought the most challenging thing was the scale factor and how to find it. I eventually figured out that CP(prime) is over CP and from there, I could find the ratio of the scale factor.