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For which segment lengths is ¯¯¯AC¯ parallel to ¯¯DE¯ ?

Answer 1

Sadie Adams

See below.

#bar(AC) |\ | bar(DE)#

then

#bar(AC)/bar(AB)=bar(DE)/bar(DB)#

and

#bar(AC)/bar(BC)=bar(DE)/bar(BE)#

and

#bar(BC)/bar(AB)=bar(BE)/bar(DB)#

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Answer 2

Savannah Aguilar

The segments ( \overline{AC} ) and ( \overline{DE} ) are parallel when the corresponding sides of the triangles ( \triangle ABC ) and ( \triangle EFD ) are proportional by the Thales' theorem. That is, when ( \frac{AD}{AB} = \frac{AE}{AC} ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.