Solved: "Does congruence of triangles have the reflexive property?..."

hexacordoK

Answered question

2021-01-10

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

Answer & Explanation

jlo2niT

Skilled2021-01-11Added 96 answers

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, $△ D E F$

$\Rightarrow △ D E F \tilde{=} △ D E F$ .
Hence, the congruence of triangle have the reflexive property.
Step 3
ii) The symmetric property of a triangle:
Consider, $△ D E F and △ P Q R$

For, $△ D E F \tilde{=} △ P Q R t h e n △ P Q R \tilde{=} △ D E F$ .
Hence, the congruence of triangle have the symmetric property.
Step 4
iii) The transitive property of a triangle:
Consider, $△ D E F and △ P Q R$

For, $△ D E F \tilde{=} △ P Q R and △ P Q R \tilde{=} △ X Y Z t h e n △ D E F \tilde{=} △ X Y Z$ .
Hence, the congruence of triangle have the transitive property.

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