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Reflexive Property

Reflexive Property

One-page printable reference

See It in Action

Two examples of the idea done right—and one common look-alike that is not right.

EXAMPLE

EXAMPLE

NON-EXAMPLE

Definition

Reflexive Property: The reflexive property states that any geometric figure (or number) is congruent or equal to itself.

Key points:

  • In algebra: a=a for any real number a.

  • In geometry: Any segment is congruent to itself AB ≅ AB, and any angle is congruent to itself ∠A ≅ ∠A.

  • Often used in proofs when two triangles share a side or an angle.

Proof Example

Given DC ≅ BA, CB ≅ AD

Prove △DCB ≅ △BAD


Quadrilateral ABCD with a diagonal drawn between B and D. The diagonal has an arrow pointing at it.

Statements

Reasons

  1. DC ≅ BA, CB ≅ AD

  2. BD ≅ DB

  3. DCB≅BAD

  1. Given

  2. Reflexive Property

  3. SSS


KEEP GOING

Learn the whole picture

This term is one piece. Our courses build it into everything around it—short videos, practice, and the “why” behind every concept.

Algebra 1

Lines, slope, functions & more

Geometry

Shapes, proofs & spatial reasoning

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