Question

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

Answer 1

`\overline {DE} \parallel \overline{AB}` because
`(EC)/(DC) = (AC)/(BC)`.

Explanation:

According to the Theorem of Thales and definition of proportionality,
`\overline {DE} \parallel \overline{AB}` if and only if
`(EC)/(DC) = (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:

`(15\,cm)/(20\,cm) = (27\,cm)/(36\,cm)`

`(3)/(4) = (3)/(4)`

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