Question

A perpendicular bisector of DC is AB and a perpendicular bisector of AB is DC. the intersection of AB and DC is at E. Which equation is true?
EB =CD
AE= DE
DE = CE
CD= CE
AB=CD

Answer 1

Answer: DE = CE

Step-by-step explanation: AB is a continuous line so the distance from A to E could be different than the distance from D to E.

Answer 2

DE = CE is true.

A perpendicular bisector is a line that divides another line into two equal parts and is also perpendicular to it.

Here, we are given that AB is the perpendicular bisector of DC and DC is a perpendicular bisector of AB.

This means that AB and DC are the perpendicular bisectors of each other at the point of intersection, that is, E.

Now, since AB bisects DC at point E

⇒ DE = CE

and similarly, DC bisects AB

⇒ AE = BE

Apart from these two equalities, we cannot infer anything else from the given information.

Thus, out of the given options, we can see that only option 3, that is, DE = CE is true.

Learn more about perpendicular bisectors here-

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