Question

which property is illustrated by this statement? if m∠a = 25° and 25° = m∠b, then m∠a = m∠b. reflexive property: a = a symmetric property: if a = b, then b = a transitive property: if a = b and b = c, then a = c distributive property: a(b + c) = ab + ac symmetric property reflexive property distributive property transitive property

Explanation:

Step1: Analyze the given statement

We have \(m\angle A = 25^{\circ}\) (so \(a = b\) where \(a=m\angle A\) and \(b = 25^{\circ}\)), \(25^{\circ}=m\angle B\) (so \(b = c\) where \(c=m\angle B\)), and then \(m\angle A=m\angle B\) (so \(a = c\)).

Step2: Compare with property definitions

The Transitive Property states "If \(a = b\) and \(b = c\), then \(a = c\)". This matches the structure of the given statement.
The Symmetric Property is about reversing equality (\(a = b\) implies \(b = a\), not a chain of two equalities leading to a third as here). The Reflexive Property is \(a=a\). The Distributive Property is about multiplication over addition (\(a(b + c)=ab+ac\)), which is unrelated to equality - chaining of angles.

Answer:

Transitive Property