Question

Identify the property that justifies the statement.

"∠xyz ≅ ∠pdq and ∠pdq ≅ ∠abc, so ∠xyz ≅ ∠abc."
Option 1: Transitive property of congruence
Option 2: Reflexive property of congruence
Option 3: Symmetric property of congruence
Option 4: Corresponding angles property

Answer 1

The statement given is justified by the Transitive Property of Congruence, which allows the conclusion that two angles are congruent based on their shared congruence with a third angle. The property that justifies the statement is the Transitive property of congruence. This property states that if two angles are congruent to the same angle, then they are congruent to each other. In this case, since ∠xyz ≅ ∠pdq and ∠pdq ≅ ∠abc, we can conclude that ∠xyz ≅ ∠abc.

Step-by-step explanation:

The statement is justified by the Transitive Property of Congruence. This property states that if one angle is congruent to a second angle, and the second angle is congruent to a third angle, then the first and third angles are also congruent. It is a fundamental concept in geometry that allows the inference of the equality of two angles or segments based on their shared relationship with a third.