Question

practice question 2
explain how you know that segment de is not parallel to segment bc (hint: check the proportions.)
(image of a triangle with points a, b, c, d, e. ad = 4, db = 2, ae = 9, ec = 5, de = 11)

Explanation:

Step1: Calculate the ratio of \( \frac{AD}{DB} \)

\( \frac{AD}{DB}=\frac{4}{2} = 2 \)

Step2: Calculate the ratio of \( \frac{AE}{EC} \)

\( AE=9, EC = 5 \), so \( \frac{AE}{EC}=\frac{9}{5}=1.8 \)

Since \( \frac{AD}{DB}
eq\frac{AE}{EC} \), by the converse of the basic proportionality theorem (Thales' theorem), \( DE \) is not parallel to \( BC \)

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 \( BC \)