Video: Congruency of Polygons

If the corresponding angles of two polygons are equal in measure, are the polygons congruent?

02:56

Video Transcript

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 rectangle.

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.

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