Question

use the information shown here to complete the proof. given each statement, provide the correct reason.

1. statement 5: ( mangle eba=mangle dbc )

a. substitution property of equality
b. given
c. division property of equality
d. angle addition postulate
given: ( mangle 1=mangle 3 )
prove: ( mangle eba=mangle dbc )

Explanation:

The Substitution Property of Equality states that if \(a = b\), then \(a\) can be substituted for \(b\) in any equation. Here, \(m\angle EBA=m\angle1 + m\angle2\) and \(m\angle DBC=m\angle3 + m\angle2\). Since \(m\angle1 = m\angle3\) (given), we substitute \(m\angle1\) with \(m\angle3\) (or vice - versa) in the equations for \(m\angle EBA\) and \(m\angle DBC\) to get \(m\angle EBA=m\angle DBC\).

Answer:

A. Substitution Property of Equality