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 transitive property symmetric property reflexive property distributive property

Explanation:

Step1: Analyze the given statement

We have \( m\angle A = 25^{\circ} \) and \( 25^{\circ}=m\angle B \), and we conclude \( m\angle A=m\angle B \). Let \( a = m\angle A \), \( b = 25^{\circ} \), \( c=m\angle B \). So the form is if \( a = b \) and \( b = c \), then \( a = c \).

Step2: Match with the properties

• Reflexive Property: \( a=a \), not matching.
• Symmetric Property: If \( a = b \), then \( b = a \), not matching.
• Transitive Property: If \( a = b \) and \( b = c \), then \( a = c \), this matches our statement.
• Distributive Property: \( a(b + c)=ab+ac \), not matching.

Answer:

Transitive Property