Question

question 2 of 10
which property is illustrated by the following statement? if △
abc≅△def, and △def≅△xyz, then △abc≅△xyz.

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

Explanation:

Step1: Recall Property Definitions

• Symmetric Property: If \( a = b \), then \( b = a \) (or for congruence, if \( \triangle ABC \cong \triangle DEF \), then \( \triangle DEF \cong \triangle ABC \)).
• Reflexive Property: Any figure is congruent to itself (e.g., \( \triangle ABC \cong \triangle ABC \)).
• Commutative Property: Usually for operations (e.g., \( a + b = b + a \)), not directly for congruence in this form.
• Transitive Property: If \( a = b \) and \( b = c \), then \( a = c \) (for congruence, if \( \triangle ABC \cong \triangle DEF \) and \( \triangle DEF \cong \triangle XYZ \), then \( \triangle ABC \cong \triangle XYZ \)).

Step2: Match the Statement to the Property

The given statement follows the form of the transitive property: if one figure is congruent to a second, and the second is congruent to a third, then the first is congruent to the third. This matches the transitive property definition.

Answer:

D. Transitive