Question

complete the proof that ( overline{i k} cong overline{h j} ).

Explanation:

Step1: Justify step 5

The formula \(m\angle HGJ=m\angle HGI + m\angle IGJ\) is based on the Additive Property of Angle Measure. This property states that if an angle is composed of two adjacent angles, then the measure of the larger angle is the sum of the measures of the two smaller adjacent angles.

Step2: Justify step 7

From step 5: \(m\angle HGJ=m\angle HGI + m\angle IGJ\), and from step 6: \(m\angle IGK=m\angle IGJ + m\angle HGI\). By the Transitive Property of Equality (if \(a = b + c\) and \(d=b + c\), then \(a=d\)), we can conclude that \(m\angle HGJ=m\angle IGK\).

Answer:

1. Additive Property of Angle Measure; 7. Transitive Property of Equality