Congruent Figures

Let’s consider these sets of figures. In which of the sets are the figures congruent to each other?

To be able to answer this, we must first know what the term congruent means.

Congruent means identical in form or coinciding exactly when superimposed. Let’s take a set of two identical figures from here. Then let’s trace the second figure using some tracing paper and place the traced copy on the first one.

We see that they both coincide exactly. Therefore, these figures are congruent to each other.

Let’s consider another set of two identical figures from here. Let’s trace the second figure here and place the traced copy on the first one.

We see that they don’t coincide exactly. Therefore, these figures are not congruent to each other.

In other words, we can say that two objects are considered congruent if they have the same size and shape. The first set of figures is congruent as they are of the same size and shape. The second set of figures is not congruent because, though they are of the same shape, they are not of the same size.

Now, look at the sets of figures given before. These two are of the same shape but of different size. Hence, they are not congruent. These two figures are of different shapes. Hence, not congruent. These two are of the same shape and size. Hence, they are congruent.

What can we say about these figures? At first these figures do not look congruent. But there’s a catch! If we rotate the second figure, like this, we see that it becomes identical to the first one. When we superimpose its traced copy on the first one, we find that they are also congruent.

Thus we can conclude that it does not matter how the figures are placed, they are considered congruent if they overlap each other on superimposing. Are only figures considered congruent?

Consider two line segments AB and CD, each measuring 5 units.

Can we say that they are congruent? Yes, we can. Segment AB is congruent to segment CD. Now, consider two angles, each measuring 60^{O}. These two angles are also congruent.