Study Guide 7.4-7.6

7.4 Showing Triangles Are Similar : SSS and SAS

Side-Side-Side Similarity Theorem

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

Side -Angle -Side Similarity Theorem

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

7.5   Proportions and Similar Triangles

Triangle Proportionality Theorem
-If a line parallel to one side of a triangle intersects the other the 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 .

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

 
 

 

 

 

 

 

7.6   Dilation
A dilation is a transformation with center C and scale factor K that maps each point P to and image p' so P' lies on segment CP and CP' = K x CP .

O= center of Dilation
A= point
A'= image

Types of Dilation
      -If the image is smaller than the original figure ,then the dilation is a REDUCTION .If the image is larger than the dilation it is an ENLARGMENT .

Scale Factor -The scale factor of a dilation is the ratio of CP' to CP.