Question

fg ≅ ij, fk ≅ hi, and jk ≅ gh. complete the proof that △fgk ≅ △ijh.
1 fg ≅ ij given
2 fk ≅ hi given
3 jk ≅ gh given
4 gk = jk + gj
5 hj = gh + gj
6 gk = gh + gj substitution
7 hj = gk transitive property of equality
8 △fgk ≅ △ijh sss

Explanation:

Step1: Segment Addition Postulate

The Segment Addition Postulate states that if \(A\), \(B\), and \(C\) are collinear points and \(B\) is between \(A\) and \(C\), then \(AC = AB+BC\). For statement \(4\), since \(J\) is between \(K\) and \(G\), \(GK=JK + GJ\).

Step2: Segment Addition Postulate

For statement \(5\), since \(G\) is between \(H\) and \(J\), by the Segment Addition Postulate, \(HJ=GH + GJ\).

Answer:

1. Segment Addition Postulate; 5. Segment Addition Postulate.