Question

AC=36cm, and BC=27cm. Verify that DE\\AB.

Answer 1

Answer:

$\overline {DE} \parallel \overline{AB}$ because $\frac{EC}{DC} = \frac{AC}{BC}$.

Step-by-step explanation:

According to the Theorem of Thales and definition of proportionality, $\overline {DE} \parallel \overline{AB}$ if and only if $\frac{EC}{DC} = \frac{AC}{BC}$. If we know that $EC = 15\,cm$, $DC = 20\,cm$, $BC = 36\,cm$ and $AC = 27\,cm$, then we have the following result:

$\frac{15\,cm}{20\,cm} = \frac{27\,cm}{36\,cm}$

$\frac{3}{4} = \frac{3}{4}$

Hence, $\overline {DE} \parallel \overline{AB}$.