In Figure, D and E are points on side BC of a ΔABC such that BD = CE and AD = AE. Show that ΔABD ΔACE.


Given: In ΔABC, BD = CE and AD = AE.

In ΔADE,


AD = AE


ADE = AED …(1) (opposite angles to equal sides are equal)


Now, ADE + ADB = 180° (linear pair)


ADB = 180° - ADE ..(2)


Also, AED + AEC = 180° (linear pair)


AEC = 180° - AED


AEC = 180° - ADE .. (3) (∵∠ADE = AED)


From (2) and (3)


ADB = AEC ..(4)


Now, In ΔADB and ΔAEC,


AD = AE (given)


BD = EC (given)


ADB = AEC (from (4)


Hence, ΔABD ΔACE (by SAS)


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