Answered

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

Are Segments EB And DC Parallel If So Explain Why And If Not Explain Why Not class=

Sagot :

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,

[tex]\frac{EA}{DA}=\frac{BA}{CA}[/tex]

Thus,

[tex]\begin{gathered} \Rightarrow\frac{8}{6+8}=\frac{6.5}{5+6.5} \\ \Rightarrow\frac{8}{14}=\frac{6.5}{11.5} \\ \Rightarrow0.571428\ldots=0.565217\ldots!!! \end{gathered}[/tex]

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

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