SIMILARITYReturn to Mathematics Index
Kee, Natalia Harlan Community Academy H.S.
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