Question

practice 2
here is a diagram.
explain how you know that segment de is not parallel to segment bc.

Explanation:

Step1: Apply the converse of the basic proportionality theorem (Thales' theorem)

If \(DE\parallel BC\), then \(\frac{AD}{DB}=\frac{AE}{EC}\)

Step2: Calculate the ratios

\(AD = 4\), \(DB=2\), so \(\frac{AD}{DB}=\frac{4}{2} = 2\)
\(AE = 9\), \(EC = 5\), so \(\frac{AE}{EC}=\frac{9}{5}=1.8\)

Step3: Compare the ratios

Since \(2
eq1.8\), the ratios \(\frac{AD}{DB}\) and \(\frac{AE}{EC}\) are not equal.

Answer:

Since \(\frac{AD}{DB}=\frac{4}{2} = 2\) and \(\frac{AE}{EC}=\frac{9}{5}=1.8\), and \(2
eq1.8\), by the converse of the basic proportionality theorem (Thales' theorem), segment \(DE\) is not parallel to segment \(BC\).