Question

Identify the property that justifies the statement.

∠ XYZ≌ ∠ PDQ and ∠ PDQ≌ ∠ ABC , so ∠ XYZ≌ ∠ ABC.
a. Add. Prop. of ≅
b. Reflex. Prop. of ≅
c. Trans. Prop. of ≅
d. Sym. Prop. of ≅

Answer 1

The correct property justifying that angle XYZ is congruent to angle ABC through a common congruent angle PDQ is the Transitive Property of Congruence.

Step-by-step explanation:

The question is asking to identify the property that justifies the statement that if angle XYZ is congruent to angle PDQ, and angle PDQ is congruent to angle ABC, then angle XYZ is congruent to angle ABC. This relationship can be justified by the Transitive Property of Congruence, which allows us to infer that if two angles are each congruent to a third one, then they are congruent to each other.

The transitive property can be applied to geometric figures, algebraic expressions, inequalities, or in various logical arguments to establish such relationships. It is one of the fundamental properties used across different branches of mathematics to make valid deductions and inferences.