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

See below.

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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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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.

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.

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.

- A triangle has corners at points A, B, and C. Side AB has a length of #8 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #9 #, what is the length of side BC?
- Check if the following are triangles? If yes name them? 1) #ΔTAR, ∠T= 184 and ∠A = 86# 2) #ΔDEZ, ∠D = 60 and ∠E = 60# 3) #ΔCHI, ∠C = 30, ∠H = 60 and ∠I = 90# 4)#ΔJMR, ∠J = 5, ∠M = 120 and ∠R = 67# 5) #ΔKLM, bar(KL) = bar(LM) = bar(MK)#
- A triangle has corners at points A, B, and C. Side AB has a length of #32 #. The distance between the intersection of point A's angle bisector with side BC and point B is #24 #. If side AC has a length of #27 #, what is the length of side BC?
- Triangle A has an area of #18 # and two sides of lengths #5 # and #9 #. Triangle B is similar to triangle A and has a side of length #12 #. What are the maximum and minimum possible areas of triangle B?
- Triangle A has an area of #6 # and two sides of lengths #4 # and #6 #. Triangle B is similar to triangle A and has a side of length #18 #. What are the maximum and minimum possible areas of triangle B?

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