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GRE Prep: Help and Review22 chapters | 185 lessons

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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.

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.

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.

This property is used when you are trying to prove two figures are congruent. If you can separate the figures and the segment, or angle in question, is the same, the reflexive property of congruence can be used in the proof.

Here is an example of showing two angles are congruent using the reflexive property of congruence:

Separating the two triangles, you can see Angle Z is the same angle for each triangle. Since they are the same angle, the angle is congruent to itself.

Let's review. The **reflexive property of congruence** is used to prove congruence of geometric figures. This property is used when a figure is congruent to itself. Angles, line segments, and geometric figures can be congruent to themselves. **Congruence** is when figures have the same shape and size.

- Congruence is when two things have the same shape and size
- The reflexive property of congruence states that a figure is congruent to itself
- The reflexive property of congruence can be used to prove the congruence of two geometric figures

After you've reviewed this lesson, you should be able to state the reflexive property of congruence and explain how it is used in geometry.

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13 in chapter 11 of the course:

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