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Reflexive Property of Congruence: Definition & Examples

Lesson Transcript
Instructor: Ellen Manchester
The reflexive property of congruence states that any geometric shape is congruent to itself. Learn about the definition of congruence and examine real-world examples of the reflexive property of congruence. Updated: 10/11/2021
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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 :

Congruence Properties of Line Segments & Angles
The Transitive Property of Similar Triangles
Right Triangle Altitudes: Applications
Reflexive Property of Equality: Definition & Examples
Flow Proof in Geometry: Definition & Examples
How to Prove Relationships in Figures using Congruence & Similarity
Two-Column Proof in Geometry: Definition & Examples
The Perpendicular Transversal Theorem & Its Converse
Symmetric Property of Equality: Definition & Examples
Substitution Property of Equality: Definition & Examples
Right Triangle | Properties & Theorems
Congruency of Isosceles Triangles: Proving the Theorem
Angle Bisector Theorem: Proof and Example
HL Theorem Examples & Proof | Hypotenuse Leg Theorem
What is a Paragraph Proof? - Definition & Examples
Congruence in Overlapping Triangles
Perpendicular Bisector Theorem: Proof and Example
Proving the Third Angle Theorem
Euclid's Axiomatic Geometry: Developments & Postulates
The Reflexive Property of Equality: Definition & Examples

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  • In the first chapter of Disquisitiones Arithmeticae, Gauss introduced the concept of congruence. He explained that he was induced to adopt the symbol "\equiv" because of the close analogy with algebra
  • Jero claims that the statement, line LR is congruent to line RL and angle CBA is congruent to angle ABC is both true by the Reflexive Property of Congruence. Explain why Jero is correct.
  • If jk is congruent to lm, then lm is congruent to jk. True False
  • Explain how to segment postulates to determine congruent segments.
  • When you say A C = A C , you are using the symmetric property of congruence. True or False?
  • Prove the reflexive property of congruence [if \overline{AB} , then \overline{AB} \cong \overline{AB} ] Statement - Reason: a. {Blank} - {Blank} b. {Blank} - Reflexive Property c. {Blank} - {Blank} Explain your proof.
  • What is the meaning of reflexive relation? And is {[1,1],[2,2],[3,3],[1,3]} is reflexive relation in the set A = {1,2,3}?
  • Why we need prime number in Fermat's Little Theorem?
  • How to prove reflexive property?
  • How to tell if a relation is reflexive symmetric or transitive?
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