Video Transcript
The square in the figure has been
rotated 90 degrees counterclockwise about the point 𝐸. Do the measures of the square’s
angles decrease, increase, or stay the same as a result of this transformation?
In the figure, we have two squares:
square 𝐴𝐵𝐶𝐷 in pink and square 𝐴 prime 𝐵 prime 𝐶 prime 𝐷 prime in
orange. Usually, when we’re dealing with
transformations, the notation of writing the letter and a dash indicates the image
of a point. For example, 𝐴 prime indicates the
image of point 𝐴. And given that we have a 90-degree
counterclockwise rotation about point 𝐸, which is the origin, that would confirm
that we have the original square above and its image below.
We now need to consider if the
angles change from the original square to its transformed image. Do the angle measures get larger,
smaller, or are they the same? Well, there are a number of ways in
which we could find the answer to this question. The first way to think of this is
that both of these polygons are squares. Squares are quadrilaterals with
four congruent sides and four congruent angles. We can see from the grid that the
sides in the polygons are horizontal and vertical. So they all meet at right
angles. In each square, the angles are all
90 degrees. So the angle measures have not
changed at each vertex during the transformation.
An alternative way to reason
through this problem is to recall that rotations are a rigid transformation. That means that the lengths are
preserved through the transformation. We can see, for example, that the
image of the square hasn’t got any larger or smaller. It is congruent to the original
shape. Therefore, the angles will stay the
same. So the measure of the angle at 𝐴
prime will be the same as the measure of angle 𝐴. And the angle measure of 𝐵 prime
will be the same as the measure of the angle at 𝐵, and so on.
We can therefore give the answer to
the question “Do the measures of the square’s angles decrease, increase, or stay the
same?” as “they stay the same.”
