Question

geometry 2 sy2026

1. makayla found the statement shown in her geometry book, \points h, n, r, t, and y are collinear where hn = nr and rt = ty.\ makayla concluded that hr = ry. select all of the diagrams that are counter - examples to makaylas conclusion.

Explanation:

Step1: Recall collinear - point and segment - length concept

Collinear points lie on the same line. We need to check if \(HN = NR\), \(RT=TY\) and \(HR
eq RY\) for counter - examples.

Step2: Analyze option A

If \(HN = NR\) and \(RT = TY\), then \(HR=HN + NR\) and \(RY=RT + TY\), so \(HR = RY\). This is not a counter - example.

Step3: Analyze option B

If \(HN = NR\) and \(RT = TY\), then \(HR=HN + NR\) and \(RY=RT + TY\), so \(HR = RY\). This is not a counter - example.

Step4: Analyze option C

If \(HN = NR\) and \(RT = TY\), but the order of points is \(H,N,Y,T,R\). Here, \(HR=HN + NR\) and \(RY\) is not equal to \(HR\) as the segments are arranged differently. This is a counter - example.

Step5: Analyze option D

The order of points is \(R,T,N,Y,H\). If \(HN = NR\) and \(RT = TY\), \(HR
eq RY\). This is a counter - example.

Step6: Analyze option E

The order of points is \(Y,T,R,N,H\). If \(HN = NR\) and \(RT = TY\), \(HR
eq RY\). This is a counter - example.

Answer:

C. Points arranged as \(H,N,Y,T,R\)
D. Points arranged as \(R,T,N,Y,H\)
E. Points arranged as \(Y,T,R,N,H\)