SIMILARITY     






Kee, Natalia                 Harlan Community Academy H.S.
14814 Ridgewood Dr.          1-312-821-2800
Oak Forest, IL 60452
1-708-535-2837

OBJECTIVES

Discover the factor of proportionality in similar polygons and to relate this factor 
to the perimeters and areas of similar polygons. 

APPARATUS NEEDED

Overhead projector, rulers for each student, protractors for each student, handouts 
of printed polygons (these are to be measured by each student). 

RECOMMENDED STRATEGY

     Students will measure each side and each angle of the polygons on the handouts.  
They will compare their measurements with the overhead projection of these polygons 
and derive a factor of proportionality between each corresponding pair of sides and 
angles of the two figures being compared. They will measure the angles of their 
polygons and compare these measurements with the corresponding angles of the 
projected similar polygon.  (Discovery: the angles retain their same measure in both 
figures-theirs and the overhead's). 

     This process can be used with different pairs of polygons to establish a factor 
of proportionality in their perimeters and areas.  Students should discover that this 
factor remains constant in similar polygons and is squared when determining areas of 
similar polygons. 

Example:Ratio of two similar polygons' corresponding sides is 1/3. 

   Perimeters of each polygon are: 2,4,2,4 = 2+4+2+4 = 12 units 
                                          3(2+4+2+4) = 36 units

 Areas of each polygon are: length x width = area in square units 
                                 2 x 4     = 8 square units
                               3(2)x 3(4)  = 72 square units