Question

in the diagram, segment $ab$ is parallel to segment $ab$.
$overline{ab}paralleloverline{ab}$
what is the length of segment $bb$?
a 3.5
b 4
c 10
d 10.5

Explanation:

Step1: Use the basic proportionality theorem (Thales' theorem)

Since \(\overline{AB}\parallel\overline{A'B'}\), we have \(\frac{BB'}{B'C}=\frac{AA'}{A'C}\).
Given \(AA' = 3\), \(A'C=6\), \(B'C = 7\), and let \(BB'=x\).
The proportion becomes \(\frac{x}{7}=\frac{3}{6}\).

Step2: Solve the proportion for \(x\)

Cross - multiply: \(6x=3\times7\).
\(6x = 21\).
Divide both sides by 6: \(x=\frac{21}{6}=3.5\).

Answer:

A. 3.5