# Properties of congruence

The three properties of congruence are the reflexive property of congruence, the symmetric property of congruence, and the transitive property of congruence. These properties can be applied to segment, angles, triangles, or any other shape.

Reflexive property of congruence

The meaning of the reflexive property of congruence is that a segment, an angle, a triangle, or any other shape is always congruent or equal to itself.

Examples

ABAB (Segment AB is congruent or equal to segment AB)

∠A ≅ ∠A (Angle A is congruent or equal to angle A)

Symmetric property of congruence

The meaning of the symmetric property of congruence is that if a figure (call it figure A) is congruent or equal to another figure (call it figure B), then figure B is also congruent or equal to figure A.

Examples

If ABCD, then CDAB

If ∠A ≅ ∠B , then ∠B ≅ ∠A

Transitive property of congruence

The meaning of the transitive property of congruence is that if a figure (call it figure A) is congruent or equal to another figure (call it figure B) and figure B is also congruent to another figure (call it C) , then figure A is also congruent or equal to figure C.

Examples

If ABCD and CDEF, then ABEF

If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C

## Naming the properties of congruence that justify the statements below.

If XYZW, then ZWXY     This is the symmetric property of congruence.

∠RTS ≅ ∠RTS    This is the reflexive property of congruence.

If GFST and STWU, then GFWU    This is the transitive property of congruence.

## Applying the properties of congruence to other shapes

Reflexive property

ABC ≅ABC (A triangle is always congruent or equal to itself)

Symmetric property

If ABCD ≅ EFGH, then EFGH ≅ ABCD

Rectangle ABCD could be the shape of your backyard and rectangle EFGH could be the shape of neighbor's backyard.

## A little exercise about the properties of congruence

Try to complete each statement using the given property

Reflexive property of congruence

∠UGD ≅ ?

Symmetric property of congruence

If SEPO, then    ?    ≅    ?

Transitive property of congruence

If ∠S ≅ ∠T and ∠   ?   ≅ ∠U, then ∠   ?    ≅ ∠   ?

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