Question

which property is illustrated by the statement given below?
△ raj ≅ △ raj

a. symmetric
b. distributive
c. transitive
d. reflexive

Explanation:

To determine the property, we analyze each option:

• Symmetric Property: If \( \triangle ABC \cong \triangle DEF \), then \( \triangle DEF \cong \triangle ABC \). This is not the case here as the triangle is congruent to itself, not another triangle.
• Distributive Property: Applies to operations like multiplication over addition (e.g., \( a(b + c)=ab + ac \)), not congruence.
• Transitive Property: If \( \triangle ABC \cong \triangle DEF \) and \( \triangle DEF \cong \triangle GHI \), then \( \triangle ABC \cong \triangle GHI \). This involves three triangles, but here we have one triangle congruent to itself.
• Reflexive Property: A figure is congruent to itself (e.g., \( \triangle ABC \cong \triangle ABC \)). The statement \( \triangle RAJ \cong \triangle RAJ \) shows a triangle is congruent to itself, so this is the reflexive property of congruence.

Answer:

D. Reflexive