Question

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

Explanation:

The symmetric property of congruence states that if one triangle is congruent to another triangle, then the second triangle is congruent to the first triangle. In this case, since \(\triangle HAX\cong\triangle RIG\), by the symmetric property, \(\triangle RIG\cong\triangle HAX\).

• The transitive property would involve three triangles (e.g., if \(\triangle A\cong\triangle B\) and \(\triangle B\cong\triangle C\), then \(\triangle A\cong\triangle C\)).
• The reflexive property is about a triangle being congruent to itself (\(\triangle ABC\cong\triangle ABC\)).
• The distributive property is an algebraic property (\(a(b + c)=ab+ac\)) and not related to triangle congruence.

Answer:

D. Symmetric