Question

In the isosceles triangle ABC, AB = AC, show that BE = EC. ​

Answer 1

⇒GIVEN:-

→A isosceles triangle ABC in which AB=AC

⇒TO PROVE:-

→BE=EC

⇒CONSTRUCTION:-

→Draw AE ⊥BC

⇒PROOF:-

AB=AC.       [given]

∴∠ABE=∠ACE.   [angle opposite to equal sides are equal ]

In ΔAEC and ΔAEB

∠ABE=∠ACE.      [Proved above]

∠AEB=∠AEC.      [each =90⁰  ∵AE⊥BC]

→We know that If two angles of a triangles are equal then 3rd angle is also equal

∴∠EAB=∠EAC

AE=AE.         [common side]

AB=AC.        [Given]

∴By SAS congruence

ΔAEC≅ΔAEB

→BE=EC.    [By cpct]

Hence proved.