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

Answer 1

#AE= 14#

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:

#x-10=2x-34# #x=24#

So now for AE: #24-10=14#

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Answer 2

Parker Allen

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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Answer from HIX Tutor

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