b Evaluate the ratio of corresponding sides in each pair of squares.
C
c What can you say about the similarity of squares looking at the table you made in Part B?
A
a See solution.
B
b See solution.
C
c Every two squares are similar polygons.
Practice makes perfect
a Let's start with drawing three different-sized squares using the ruler. Let square ABCD have side lengths of 1 cm, square PQRS have side lengths of 2 cm, and WXYZ have side lengths of 4 cm.
b Now, we are asked to evaluate the ratios of corresponding sides for each pair of squares. Let's use a table.
ABCD & PQRS
PQRS & WXYZ
ABCD & WXYZ
AB/PQ=1/2
PQ/WX=2/4
AB/WX=1/4
BC/QR=1/2
QR/XY=2/4
BC/XY=1/4
CD/RS=1/2
RS/YZ=2/4
CD/YZ=1/4
DA/PS=1/2
PS/ZW=2/4
DA/ZW=1/4
As we can see, the ratios between the corresponding sides in each pair of squares we draw are constant. This means that each pair of squares we drew is a pair of similar polygons as all squares have four right angles.
c Since each square has four congruent sides, the ratio between the corresponding sides of two squares will be always constant. Therefore, we can assume that every two squares are similar polygons.
