Question

use the given statement bank to fill in the following two - column proof. two have been done for you. given: ( mangle1=mangle3 ) prove: ( mangle ptr=mangle stq ) statements ( mangle1 = mangle3 ) ( mangle2 = mangle2 ) ( mangle1 + mangle2 = mangle3 + mangle2 ) ( mangle1 + mangle2 = mangle ptr ) ( mangle3 + mangle2 = mangle stq ) ( mangle ptr = mangle stq ) reasons given addition property of equality

Explanation:

Step1: Reflexive Property of Equality

$$m\angle2 = m\angle2$$

Step2: Angle Addition Postulate

$$m\angle1 + m\angle2 = m\angle PTR$$
$$m\angle3 + m\angle2 = m\angle STQ$$

Step3: Substitution Property of Equality

Since \(m\angle1 + m\angle2 = m\angle3 + m\angle2\), and \(m\angle1 + m\angle2 = m\angle PTR\), \(m\angle3 + m\angle2 = m\angle STQ\), then \(m\angle PTR = m\angle STQ\)

Answer:

The reason for \(m\angle2 = m\angle2\) is Reflexive Property of Equality. The reason for \(m\angle1 + m\angle2 = m\angle PTR\) and \(m\angle3 + m\angle2 = m\angle STQ\) is Angle Addition Postulate. The reason for \(m\angle PTR = m\angle STQ\) is Substitution Property of Equality