Does congruence of triangles have the reflexive property? the symmetric property? the transitive property?

Step1
Given:
The congruence of triangles.
Step 2
To identify whether the congruence of triangles have the reflexive property, the symmetric property, and the transitive property.
i) The reflexive property of a triangle:
Consider, ${\displaystyle \mathrm{△}DEF}$

${\displaystyle \Rightarrow \mathrm{△}DEF\stackrel{\sim }{=}\mathrm{△}DEF}$.
Hence, the congruence of triangle have the reflexive property.
Step 3
ii) The symmetric property of a triangle:
Consider, ${\displaystyle \mathrm{△}DEF\text{and}\mathrm{△}PQR}$

For, ${\displaystyle \mathrm{△}DEF\stackrel{\sim }{=}\mathrm{△}PQRthen\mathrm{△}PQR\stackrel{\sim }{=}\mathrm{△}DEF}$.
Hence, the congruence of triangle have the symmetric property.
Step 4
iii) The transitive property of a triangle:
Consider, ${\displaystyle \mathrm{△}DEF\text{and}\mathrm{△}PQR}$

For, ${\displaystyle \mathrm{△}DEF\stackrel{\sim }{=}\mathrm{△}PQR\text{and}\mathrm{△}PQR\stackrel{\sim }{=}\mathrm{△}XYZthen\mathrm{△}DEF\stackrel{\sim }{=}\mathrm{△}XYZ}$.
Hence, the congruence of triangle have the transitive property.