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Reflexive Property of Congruence: Definition & Examples

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  • 0:01 Reflexive Property of…
  • 1:33 Showing Congruence
  • 2:24 Lesson Summary
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Lesson Transcript
Instructor: Ellen Manchester
In this lesson, we will look at the reflexive property of congruence. It is used to prove congruence when dealing with geometric figures. Specifically, the reflexive property is used when a figure is congruent to itself.

Reflexive Property of Congruence

The reflexive property of congruence states that any geometric figure is congruent to itself.

Congruence means the figure has the same size and shape. If you were comparing something to itself, then it would most definitely have the same size and shape. Geometric figures, line segments, angles, and geometric shapes can all show congruence. If a line segment has the same length, the line segments would be congruent. If an angle has the same angle measure, the angles would be congruent. If we had a triangle with the same side lengths and angle measures, the triangles would be congruent.

The reflexive property of congruence shows that any geometric figure is congruent to itself. A line segment has the same length, an angle has the same angle measure, and a geometric figure has the same shape and size as itself. The figures can be thought of as being a reflection of itself.

The symbol for congruence is :

For instance, if we were looking at angle A, because of the reflexive property of congruence, we could say angle A is congruent to angle A.

The reflexive property of congruence can also be used for line segments. Look at this figure:

Line segment LM is congruent to itself. It has the same shape and size.

The reflexive property can also be used with geometric figures, like this triangle:

Triangle ABC is congruent to triangle ABC.

Showing Congruence

On this geometric figure, we can use the reflexive property of congruence to show this:

The line segment CE is a reflection of itself. If we separated these two triangles, we can show the line segment is the same line segment because of the reflexive property of congruence.

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