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

Does congruence of triangles have the reflexive property? the symmetric property? the transitive property?
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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, $\mathrm{△}DEF$

$⇒\mathrm{△}DEF\stackrel{\sim }{=}\mathrm{△}DEF$.
Hence, the congruence of triangle have the reflexive property.
Step 3
ii) The symmetric property of a triangle:
Consider, $\mathrm{△}DEF\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{△}PQR$

For, $\mathrm{△}DEF\stackrel{\sim }{=}\mathrm{△}PQRthen\mathrm{△}PQR\stackrel{\sim }{=}\mathrm{△}DEF$.
Hence, the congruence of triangle have the symmetric property.
Step 4
iii) The transitive property of a triangle:
Consider, $\mathrm{△}DEF\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{△}PQR$

For, $\mathrm{△}DEF\stackrel{\sim }{=}\mathrm{△}PQR\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\mathrm{△}PQR\stackrel{\sim }{=}\mathrm{△}XYZthen\mathrm{△}DEF\stackrel{\sim }{=}\mathrm{△}XYZ$.
Hence, the congruence of triangle have the transitive property.