Question

complete the proof that (\triangle efjcong\triangle hig).

Explanation:

Step1: Identify the property for statement 4

The formula \( FJ = IJ+FI \) is based on the Additive Property of Length. This property states that if a segment \( FJ \) is composed of two adjacent segments \( IJ \) and \( FI \), then the length of \( FJ \) is the sum of the lengths of \( IJ \) and \( FI \).

Step2: Identify the property for statement 7

From statement 5 \( GI = FG + FI \) and statement 6 \( FJ=FG + FI \), by the Transitive Property of Equality (if \( a=b \) and \( b = c \), then \( a=c \)), since \( GI\) and \( FJ \) are both equal to \( FG + FI \), we can conclude \( GI = FJ \).

Answer:

1. Additive Property of Length
2. Transitive Property of Equality