Question

which property is illustrated by the following statement? if $\triangle hxa \cong \triangle rgi$, then $\triangle rgi \cong \triangle hxa$. a. symmetric b. transitive c. reflexive d. commutative

Explanation:

Step1: Recall properties of congruence

The symmetric property of congruence states that if one figure is congruent to a second figure, then the second figure is congruent to the first figure. Mathematically, if \( \triangle ABC \cong \triangle DEF \), then \( \triangle DEF \cong \triangle ABC \).

Step2: Analyze the given statement

The given statement is: If \( \triangle HXA \cong \triangle RGI \), then \( \triangle RGI \cong \triangle HXA \). This matches the definition of the symmetric property of congruence.

• The transitive property (B) requires three figures: if \( \triangle A \cong \triangle B \) and \( \triangle B \cong \triangle C \), then \( \triangle A \cong \triangle C \), which is not the case here.
• The reflexive property (C) states that a figure is congruent to itself (\( \triangle A \cong \triangle A \)), which is not what's shown here.
• The commutative property (D) is more about operations (like addition or multiplication) being order - independent, not congruence of triangles.

Answer:

A. Symmetric