Question

statements: tu || xw, ∠utv ≅ ∠xwv, ∠tvu ≅ ∠wvx, △tvu ~ △wvx, ? , 14/xw = 4/7, 7(14)=(xw)(4), xw = 8. reasons: given, alternate angles theorem, vertical angles theorem, aa, ? , substitution property of equality, cross product, division property of equality. which step is missing? a. statement: tu/xw = tv/wv reason: corresponding sides of similar triangles are proportional. b. statement: tu/xw = uv/vx reason: corresponding sides of similar triangles are proportional. c. statement: tu/xw = tv/vx reason: corresponding sides of similar triangles are proportional. d. statement: tu/xw = uv/wv reason: corresponding sides of similar triangles are proportional.

Explanation:

Step1: Analyze the similarity - related content

Since we know that $\triangle TVU\sim\triangle WVX$ (by AA similarity), and corresponding sides of similar triangles are proportional. Given $\overline{TU}\parallel\overline{XW}$, we have angle - angle relationships.

Step2: Determine the missing step

Before using the division property of equality $\frac{XW}{7}=\frac{14}{4}$, we should get to the cross - product step. If we start from the proportion of corresponding sides of similar triangles $\frac{XW}{TU}=\frac{WV}{TV}$, substituting the known values and cross - multiplying gives us the step before the division step.

Answer:

Cross - product of corresponding sides of similar triangles.