Question

Are segments EB and DC parallel? if so, explain why and if not, explain why not.

Answer 1

Suppose that EB and DC are parallel; therefore, triangles EAB and DAC are similar triangles due to the AAA postulate. Because those two triangles are similar, the ratio between their corresponding sides is constant; then,

`(EA)/(DA)=(BA)/(CA)`

Thus,

`\begin{gathered} \Rightarrow(8)/(6+8)=(6.5)/(5+6.5) \\ \Rightarrow(8)/(14)=(6.5)/(11.5) \\ \Rightarrow0.571428\ldots=0.565217\ldots!!! \end{gathered}`

The two quantities are not the same, this is a contradiction. Thus, EB and DC cannot be parallel.