Question

in triangle trs, vz = 6 inches. what is rz?
options: 3 inches, 6 inches, 12 inches, 18 inches

Explanation:

Step1: Identify midsegments

V, W, U are midpoints (marked congruent segments). VZ connects midpoints of TR and TS, so VZ is midsegment of △TRS.

Step2: Apply midsegment theorem

Midsegment length = ½ base length. Here, VZ = ½ RS. But wait—wait, the question asks for RZ? No, wait the problem says "What is RZZ?" Probably typo: RZ? No, wait VZ is midsegment to RS? Wait no, looking at the triangle: V is midpoint of TR, W midpoint of RS, U midpoint of TS. Z is intersection of medians? Wait no, the congruent marks: TV=VS, SW=WR, TU=UR? Wait no, the problem states VZ=6 inches. Wait actually, if VZ is a midsegment parallel to RS, then RS=2VZ=12. But wait the options: 3,6,12,18. Wait maybe Z is centroid? Centroid divides median into 2:1. If VZ is 6 (shorter part), then RZ=12? Wait yes, centroid theorem: centroid divides each median into ratio 2:1 (longer segment from vertex). So if VZ=6 (segment from midpoint V to centroid Z), then RZ=2VZ=12.

Answer:

B. 12 inches