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Question

In the given figure, if x=y and AB=CB, then AE is _____.



A

less than CD

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B

greater than CD

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C

equal to CD

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D

data insufficient

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Solution

The correct option is C

equal to CD


Consider ΔABE and ΔCBD for congruency
Here, x=y
So, 180x=180y
AEB=CDB
AB = CB (Given)
CBD=ABE ( common angle of ΔABE and ΔCBD)
So, ΔABEΔCBD (by A.A.S. as the common side is not included in between the equal angles)
Therefore, AE = CD (CPCT).


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