# In the figure below, find #bar(AE)# if #bar(AC)# is a perpendicular bisector of #bar(DE)#?

Look at the picture.

By the definition of a perpendicular bisector, we can conclude that angle B is a right angle and DB=BE, and AB is a common line segment shared by both triangles above. Using SAS (Side-Angle-Side), we can conclude that both the triangles are congruent, therefore:

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To find the length of segment AE, we can use the properties of perpendicular bisectors. Since AC is a perpendicular bisector of DE, it divides DE into two congruent segments. Therefore, DE is divided into two equal parts at point C.

Given that AE = 8 units and CE = 4 units, according to the properties of perpendicular bisectors, AE is equal to CE. So, AE = CE = 4 units.

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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.

- What is the difference between a bisector and a perpendicular bisector?
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- A triangle has corners A, B, and C located at #(1 ,4 )#, #(2 ,1 )#, and #(5 , 2 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has corners A, B, and C located at #(4 ,7 )#, #(3 ,5 )#, and #(6 ,1 )#, respectively. What are the endpoints and length of the altitude going through corner C?
- A triangle has vertices #A(7 ,6 )#, #B(8 ,3 )# and #C(5 ,1 )#. What are the endpoints and length of the altitude going through vertex C?

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