Question

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step reason

1. x is the midpointvy. y is the midpointyz. given
2. ________ definition of midpoint
3. vx≅yz transitive property of congruence

q.e.d.

1. given that point b lies on the segment ac and that point b is the midpoint of ac. which is the appropriate statement for the reason in the proof?

Explanation:

Step1: Recall mid - point property

If \(X\) is the mid - point of \(\overline{VY}\), then \(\overline{VX}\cong\overline{XY}\). If \(Y\) is the mid - point of \(\overline{YZ}\), then \(\overline{XY}\cong\overline{YZ}\).

Step2: Fill in the blank

Based on the above, the missing statement for step 2 is \(\overline{VX}\cong\overline{XY}\) and \(\overline{XY}\cong\overline{YZ}\) because of the definition of mid - point.

Answer:

\(\overline{VX}\cong\overline{XY}\) and \(\overline{XY}\cong\overline{YZ}\)