Line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional
Parallel lines theorem
In the given diagram,
If
[tex]\frac{|AB|}{|ED|} =\frac{|AC|}{|EC|}[/tex]
Then,
Line AE is parallel to line BD
From the given information,
|AB| = x = 9
|ED| = 5
|AC| = 9 + 11 = 20
|EC| =5 + 7 = 12
Thus,
[tex]\frac{9}{20}=\frac{5}{12}[/tex]
20 × 5 = 9 × 12
100 ≠ 108
∴ The lines are not parallel
Hence, line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional
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