Study Guide 7.4-7.6

7.4-

SSS Similarity Postulate- If the corresponding sides of two triangles are proportional, then, the two triangles are similar.

SAS Similarity Postulate- If an angle of one triangle is congruent to an angle of a second triangle and the length of the sides that include these angles are proportional, then the triangles are similar.

Symbols- If <x is congruent to <m and PM/ZX = MN/XY, then triangle XYZ is similar to triangle MNP

7.5- Proportions and Similar Triangles

Proportionality- 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

Symbols- In triangle QRS, if TU is parallel to RS, then RT/TQ = RU/US

Converse of the Triangle Proportionality Theorem- If a line divides two sides of a triangle proportionally, then it is parallel to the third side

Symbols- In triangle QRS, if RT/TQ = RU/US, then TU is parallel to QS

The Mid-segment Theorem- The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long

Symbols- In triangle ABC, if CD = DA, and CE = EB, then DE is parallel to AB and DE = 1/2 AB

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' so that P' lies on CP and CP' = 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 than the original, then the dilation is a reduction
If the image is LARGER than the original, then the dilation is an enlargement

Scale Factor-
The scale facts of a dilation is the ratio of CP' to CP. This ratio is also the scale factor of triangle P'Q'R' to triangle PQR.