Question

given: (overline{gh}paralleloverline{ij}), (overline{gh}congoverline{ij}), (overline{gk}congoverline{il}) prove: (angle ihkcongangle gjl)

Explanation:

Step1: Identify the property for step 7

Segment Addition Postulate states that if \(A\), \(B\), and \(C\) are collinear points and \(B\) is between \(A\) and \(C\), then \(AB + BC=AC\). For line segments \(\overline{GL}\) with points \(G\), \(K\), \(L\) and \(\overline{IK}\) with points \(I\), \(L\), \(K\), we can write \(GK + KL = GL\) and \(IL+LK = IK\) using the Segment Addition Postulate.

Step2: Justify step 8

Since \(GK\cong IL\) (given) and \(KL = LK\) (reflexive property of congruence, \(a=a\)), by substitution (if \(a = b\) and \(c=d\), then \(a + c=b + d\)) into \(GK + KL = GL\) and \(IL+LK = IK\), we get \(GL=IK\) (or \(\overline{GL}\cong\overline{IK}\))

Answer:

1. Segment Addition Postulate
2. Substitution Property (using \(GK\cong IL\) and \(KL = LK\))