If the corresponding angles of two
polygons are equal in measure, are the polygons congruent?
Let’s make some sketches to find
out. We need two polygons, where
corresponding angles are equal in measure. I know that a rectangle is a
polygon and that all the angles inside rectangles are right angles. Then, I draw another rectangle. And because it is a rectangle, all
the interior angles measure 90 degrees. They are right angles.
So far, all we know about these two
rectangles is that their corresponding angles are equal. We do not know the lengths or the
widths of these rectangles. We’re working to find out for sure
if these are congruent figures. In order for us to confirm that
these two polygons are congruent, we need to prove that they are the same shape and
the same size.
Because of the interior angle
measures and the number of sides they have, we can confirm that they are the same
shape. They’re both rectangles. How can we ever confirm if they’re
the same size? Without more information, we really
don’t know. But let me show you something
else. Let’s draw a third rectangle.
Is the polygon in pink a
rectangle? Yes, it is. All the corresponding angles in the
pink rectangle are equal in measure to the blue and yellow rectangle. We don’t know its length and we
don’t know its width. By visually inspecting it, we can
determine that the pink rectangle is not the same size as the blue or the yellow
All three of these rectangles are
the same shape. But they’re not the same size. Equivalent corresponding angles in
polygons is not enough to prove that they are congruent because we can’t prove that
they are the same size. Sometimes they would be the same
size and sometimes they wouldn’t be.
Are two polygons congruent just
because the corresponding angles are congruent? No.