Question

question 9 of 10
which property is illustrated by the following statement?
if \\( \triangle h x a \cong \triangle r g i \\), then \\( \triangle r g i \cong \triangle h x a \\).
a. transitive
b. symmetric
c. reflexive
d. commutative

Explanation:

• Transitive property: If \(a = b\) and \(b = c\), then \(a = c\). This is not the case here as we have only two triangles and a single equality relation being reversed.
• Symmetric property: If \(a=b\), then \(b = a\). In the context of triangle congruence, if \(\triangle HXA\cong\triangle RGI\), then \(\triangle RGI\cong\triangle HXA\) follows the symmetric property (where \(a=\triangle HXA\), \(b = \triangle RGI\)).
• Reflexive property: \(a=a\). Here we are dealing with two different triangles, so this property is not relevant.
• Commutative property: Usually applies to operations like \(a + b=b + a\) or \(a\times b = b\times a\) (not to congruence relations of geometric figures in the way presented).

Answer:

B. Symmetric