What does congruent mean in geometry

For the first three ways, congruent figures stay congruent. Rotate the Queen of Spades, and she is still the Queen. Slide the card around the table, and our Queen is still congruent with the other playing card.

If we enlarge or shrink the Queen, it is still the same shape, but they are now different sizes. The shapes still have congruent angles, but the line segments that make up the card are now different lengths, so the two shapes are no longer congruent.

Dilating one of two congruent shapes creates similar figures , but it prevents congruency. Figures are similar if they are the same shape; the ratios and length of their corresponding sides are equal. So, are congruent figures similar? Technically, yes, all congruent figures are also similar shapes. But not all similar shapes have congruency. In geometry, similar triangles are important, and three theorems help mathematicians prove if triangles are similar or congruent.

Usually, we reserve congruence for two-dimensional figures, but three-dimensional figures, like our chess pieces, can be congruent, too.

Think of all the pawns on a chessboard. They are all congruent. The geometric figures themselves do not matter. You could be working with congruent triangles, quadrilaterals, or even asymmetrical shapes. Here are two congruent figures:.

To summarize, congruent figures are identical in size and shape; the side lengths and angles are the same. They can be rotated, reflected, or translated, and still be congruent. They cannot be dilated enlarged or shrunk and be congruent. The word 'congruent' means 'exactly equal' in terms of shape and size. Even when we turn, flip, or rotate the shapes , they remain equal. For example, draw two circles of the same radius, then cut them out and place them on one another.

We will notice that they will superimpose each other, that is, they will be placed completely over each other. This shows that the two circles are congruent. The following circles are said to be congruent since they have an equal radius , and they can be placed exactly over one another. The congruence of any two figures can be seen if they can be placed exactly over each other. The word 'congruence' is used to express the relationship of two figures that are said to be congruent.

In other words, if any two geometrical figures can be superimposed on each other, they are termed as congruent figures. This property applies to all figures like triangles , quadrilaterals , and so on.

Apart from figures, line segments and angles are also termed as congruent if they are of equal measure. Observe the following figure to understand what congruent figures mean. There is a difference between congruent and similar figures. Congruent figures have the same corresponding side lengths and the corresponding angles are of equal measure. However, similar figures may have the same shape, but their size may not be the same.

For example, observe the following triangles which show the difference between congruent and similar figures. In the congruent figures, we can see that all the corresponding sides and angles are of equal measure. However, if we notice the similar figures, we see that the corresponding angles are of equal measure, but the sides are not of equal length. Two triangles are said to be congruent if their sides are equal in length, the angles are of equal measure, and they can be superimposed on each other.

This means that the corresponding angles and corresponding sides in both the triangles are equal. Example 1: The two quadrilaterals shown below are congruent. In the following figure, you will see that the following pairs are congruent:.

You can determine the congruence of triangles by using their angles together with the congruence of their sides.

Two triangles will be equal if any of the following conditions are true:. To do this, you must first draw an angle with a ruler and then use a compass to copy the angle. The important thing is to make sure they both maintain the same angle, as this is the definition of congruence.

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