12. The diagonal of a square is the same length as its side.
A square has four equal sides and at least one right angle. When observing the diagonals of a
square, they “look” like the same length of each of the sides. This visual misinterpretation is
common.
Example of Misinterpretation:
In the square ABCD students may say
that AB = BD
Suggested Remedy:
In an activity, Students can build a specific square of given dimensions using straws.
They can measure and cut pieces representing the diagonals. By comparing the pieces of
straws which represent a side with one which represent a diagonal they will be able to see
that the lengths are different. By repeating with squares of various sizes they will
conclude that the diagonal is always longer than the side of a given square.
The misconception can also be resolved by demonstrating on a white/blackboard. Draw a
square with specific dimensions and draw in the diagonals. By placing a stick on the
diagonal adjust the length of the stick to be the same. Students can now be shown that
when the stick, which represents the diagonal of the square, is place on one side of the
same square there is a difference in their lengths.
Students can also experiment in their own books by constructing various squares and
with the use of a ruler, measure the individual sides and diagonals. Conclusions can then
be made.