A state department of education, as a question on the public-release form of a statewide standardized test, released a question to the public in which third graders have to identify congruent and similar polygons by visual inspection.
Sometimes we have to determine whether a polygon is congruent or similar to another polygon just by looking at the two polygons.
There are different ways that we can compare figures. One way is to count the number of sides. You probably know the names for some of these figures.
Triangle: 3 sides
Quadrilateral: 4 sides
Pentagon: 5 sides
Hexagon: 6 sides
Congruent figures
We can compare figures that have the same number of sides directly. If we have two triangles, we can check to see if they are congruent.
Congruent is a math word that means exactly the same shape and exactly the same size.
The triangles may be flipped over or moved around, but as long as they are the same shape and size, they are said to be congruent.
One way to check is to cut out one of the triangles and try to place it over the other one. If they match up exactly, they’re congruent.
Sometimes you can’t cut out the figures, so you need to try to match them up in your mind. Another way would be if you have a ruler, you can measure the sides of the shapes and match them up that way.
For example, the two triangles below are congruent, because they are exactly the same shape and size. Yes, one of them is rotated from the other, but if you rotated it back, you would see that one fits exactly on top of the other. That means they’re congruent.
Similar figures
Some figures look quite a bit alike, but they’re not the same size. They may be similar figures.
Similar figures have the same shape, but the sides may not be the same size.
If we have two triangles, for example, we can check to see if they’re similar. One way to see is to cut out the smaller triangle and then to place it in the center of the other triangle. If there’s an equal amount of space all around the smaller triangle, then the triangles are similar.
Another way to check is to match up the angles of the two triangles. If the angles all match, then the triangles are similar.
The drawing below has two pairs of similar triangles. On the left, we can see that there’s an equal amount of space all around the smaller triangle. That means the two triangles in the drawing on the left are similar.
And in the drawing on the right, we have placed the smaller triangle so that the top angle is right on top of the top angle in the bigger triangle. This shows that all the angles match, so it also shows that the two triangles in the diagram at the right are similar.
If you need additional practice on this subject, please visit our online card catalog at VoxLearn.org and search for “congruent” or “similar polygons.”