Question

1 fg ≅ ij given
2 fk ≅ hi given
3 jk ≅ gh given
4 gk = jk + gj definition of equilateral triangle
5 hj = gh + gj definition of angle bisector
6 gk = gh + gj additive property of length
7 hj = gk definition of angle bisector
8 △fgk ≅ △ijh definition of equilateral triangle
definition of midpoint
vertical angle theorem

Explanation:

Step1: Analyze the problem

We need to find the correct property for the given equations.

Step2: Recall the Additive Property of Length

The Additive Property of Length states that if we have three collinear points \(A\), \(B\), and \(C\) with \(B\) between \(A\) and \(C\), then \(AC=AB + BC\).
In the case of \(GK = JK+GJ\) and \(HJ = GH + GJ\), if we assume the points are arranged in a linear fashion (for the segments), the property that justifies these equations is the Additive Property of Length.

Answer:

Additive Property of Length