Question

which step is missing?
a. statement: \\( \frac { x w } { u t } = \frac { v w } { x v } \\) reason: corresponding sides of similar triangles are proportional.
b. statement: \\( \frac { x w } { u t } = \frac { x v } { u v } \\) reason: corresponding sides of similar triangles are proportional.
c. statement: \\( \frac { x w } { u t } = \frac { u v } { v w } \\) reason: corresponding sides of similar triangles are proportional.
d. statement: \\( \frac { x w } { u t } = \frac { u v } { x v } \\) reason: corresponding sides of similar triangles are proportional.

Explanation:

Step1: Recall the property of similar triangles

For similar triangles \(\triangle TVU\sim\triangle WVX\), the corresponding sides are proportional.

Step2: Identify the corresponding sides

In \(\triangle TVU\) and \(\triangle WVX\), \(XW\) corresponds to \(UT\), \(XV\) corresponds to \(UV\). So the proportion should be \(\frac{XW}{UT}=\frac{XV}{UV}\) based on the property that corresponding sides of similar triangles are proportional.

Answer:

B. Statement: \(\frac{XW}{UT}=\frac{XV}{UV}\) Reason: Corresponding sides of similar triangles are proportional.