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Congruence Properties of Line Segments & Angles

Instructor: Usha Bhakuni

Usha has taught high school level Math and has master's degree in Finance

This lesson discusses the concept of congruence with the help of relevant examples. You will also learn about the reflexive, symmetric and transitive properties of congruence related to line segments and angles.

Congruence

Suppose there are two rectangular plots of land, and both have the same area: 1200 square meters. Can you say that these plots are exactly the same? Not with this information. You need to know the length and width of each one to determine whether they are exactly the same or not.

Let's say plot A is 30 m long and 40 m wide, and plot B is 20 m long and 60 m wide.


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Imagine if we place plot A over plot B. Will it cover it entirely? No, not even if we rotate it in any direction.

Now, let's consider another scenario in which plot A is 30 m long and 40 m wide, and plot B is 40 m long and 30 m wide.


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In this case, imagine if we rotate plot A by 90 degrees, and then place it above plot B. It will entirely cover plot B.

This is the concept of congruence in geometry. If two figures are such that one figure covers the other one entirely when placed one above the other, they are called congruent figures.

In this lesson, we will apply the properties of congruence to line segments and angles.

Properties of Congruence

Suppose there are three friends: Jane, Mary and Dave. Let's consider the three properties of congruence using the height of each person.

1. Reflexive Property

Reflexive means comparing the quantity to itself. It simply states that a figure is congruent to itself. In our example, Jane's height is equal to Jane's height.

Consider the line segment AB:


Line segment AB


By the reflexive property,


Reflexive property


Now, consider the angle ABC:


Angle ABC


According to the reflexive property,


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2. Symmetric Property

The symmetric property states that if one figure is congruent to another, then the second figure is also congruent to the first. If Jane's height is equal to Dave's height, then it also means that Dave's height is equal to Jane's height.

Consider two equal line segments, AB and CD:


Two equal line segments


By the symmetric property,


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Consider two equal angles, ABC and PQR:


Two equal angles


According to the symmetric property,


Symmetric property


3. Transitive Property

The transitive property states that if a figure is congruent to another, and the second figure is congruent to a third figure, then the first figure is also congruent to the third. If Jane's height is equal to Dave's height, and Dave's height equals Mary's height, then it means that Jane's height is equal to Mary's height.

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