Here are the properties of congruence. Some textbooks list only a few, others list them all. These are analogous to the properties of equality for real numbers. Here we show congruences of angles, but the properties apply just as well to congruent segments, triangles or other geometric objects. In this article, we will describe the symmetric property of equality, the symmetric property of congruence, the symmetric property of relations, and the symmetric property of matrices. We will solve various examples related to symmetric property to better understand the concept. With the symmetric property of congruence, we can write CD = AB = 5cm. CD = 5cm The symmetric property of congruence states that if one geometric figure is congruent to another, we can say that the second figure is congruent to the first figure. For example, if the triangle ABC is congruent to the triangle PQR, we can also say that the triangle PQR is congruent to the triangle ABC. Another example of the symmetric property of congruence is that if one line segment AB is congruent to another CD line segment, we can say that CD is congruent to AB. We can use this property for angles and other geometric figures.
All symmetric properties are specific cases of the symmetric property of relations. For example, if we define a relation on the set of numbers as “is equal”, then we get the symmetric property of equality. If the relation is defined on the set of geometric/triangle figures, then we obtain the symmetric property of congruence. Let`s discuss the symmetric property of equality in the next section. We can prove the symmetric property of the relation by assuming that one element is related to another, and then prove that the latter is also related to the first. The three properties of congruence are the reflexive property of congruence, the symmetric property of congruence, and the transitive property of congruence. These properties can be applied to segments, angles, triangles, or any other shape. Solution: Since Mary`s height is equal to Jane`s, we can write Mary = Jane.
With the symmetric property of equality, we can now write Jane = Mary. Example 3: If Mary`s size is Jane`s, can we say Jane`s size is Mary`s? Answer: Yes, we can say that Jane`s height is Mary`s. If ∠ A ≅ ∠ B and ∠ B ≅ ∠ C , then ∠ A ≅ ∠ C. Solution: Since the line segment AB is congruent to the line segment CD, we have AB = CD and AB = 5 cm. Example 2: If the line segment AB is congruent to the CD line segment and AB = 5 cm, then you will find the length of the CD. If two angles are both congruent to a third angle, then the first two angles are equally congruent.