Name the property of congruence that justifies this statement if ∠a= ∠b and ∠b = ∠c then ∠a = ∠c
The property of congruence that justifies this statement is the Transitive Property of Congruence. According to this property, if two angles are congruent to the same angle, then they are congruent to each other.
The property of congruence that justifies this statement is the Transitive Property of Congruence.
The property of congruence that justifies the statement "if ∠a = ∠b and ∠b = ∠c, then ∠a = ∠c" is the Transitive Property of Congruence.
The Transitive Property of Congruence states that if two angles are congruent to a third angle, then they are congruent to each other. In this case, since ∠a is congruent to ∠b and ∠b is congruent to ∠c, we can conclude that ∠a is congruent to ∠c.
To see why this is true, you can use the definitions and properties of angles. Two angles are congruent if they have the same measure. Therefore, if ∠a has the same measure as ∠b, and ∠b has the same measure as ∠c, then ∠a must have the same measure as ∠c. This is because equality is transitive, meaning that if a = b and b = c, then a = c.
Therefore, by applying the Transitive Property of Congruence, we can conclude that if ∠a = ∠b and ∠b = ∠c, then ∠a = ∠c.