Subject: Geometry

Congruent Figures

Congruent figures refer to two geometrical figures that have strictly the same size and shape - regardless of its position or orientation in space. For two-dimensional figures, we are referring to polygons? which are characterized mainly by angles and sides, and thus congruent polygons or congruent figures in two-dimensional space must have the same angles and sides.

Conguent Polygons

If two polygons have the same sides (number and measure) and angles, then they are said to be congruent. In the figure below, we have two triangles.

At first glance, you may say that the triangles above are not congruent. But, if you meticulously measure each sides and angles, they are equal! Thus they are congruent. In words, the right triangle on the right above is congruent to the triangle on the left.

Notation

When two figures are congruent, it is sometimes burdensome to write the word 'is congruent to' when we simply mean the two figures' congruence. Mathematics has a way to do this by the congruent sign - \cong .

So when figures A and B are said to be congruent, then we don't have to write the phrase A is congruent to B. Instead, we can write this more simply as;

A \cong B

How to tell if two polygons are congruent

Sometimes, we rely too much on our eyes in justifying things such as congruence. Like the two triangles above, we may say that they aren't congruent at first look, which is exactly not the case. Of course there will two polygons that are obvious enough for our eyes to tell the difference but for two polygons that has a very close resemblance in terms of sides and angles, we will resort to a more scientific method.