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.

 

 

Study Guide 7.1-7.3

7.1   Ratio and Proportion

-A ratio is a comparison of a number a and a nonzero number b using division .
              -Ratios can be written in 3 way . (a to b ... a/b ... a:b)
-A proportion is an equation that states that two ratios are equal.
             

The numbers b and c are the means , and the numbers a and d are the extremes of the proportion .

Cross Product Property - In a proportion ,the product or the extremes is equal to the product of the means .  (a x d =c x d)

7.2    Similar Polygons

In geometry ,two figures that have the same shape are called similar .

Two polygons are SIMILAR POLYGONS if the corresponding angles are congruent and corresponding side lengths are proportional .

 If two polygons are similar ,then the ratio of the lengths of two corresponding sides is called the SCALE FACTOR.

Perimeters of Similar Polygons
     - If two polygons are similar ,then the ratio of their perimeters is equal to the ratio of their corresponding side lengths .

7.3 Showing Triangles Are Similar : AA

Angle -Angle Similarity Postulate (AA)
- If two angles of one triangle are congruent to two angles of another triangle ,then the two triangles are similar .