Q. 184.0( 2 Votes )

ABC is a triangle in which AB=AC. If the bisectors of B and C meet AC and AB in D and E respectively, prove that BD=CE.


Answer :

Given: AB=AC and BD and AB are angle bisectors of B and C


To prove: BD = CE


Proof:


In ∆ABD and ∆ACE,


ABD = B


And ACE = C


But B = C as AB = AC … As in isosceles triangle, base angles are equal


ABD = ACE


AB = AC


A = A


Thus by ASA property of congruence,


∆ABD ACE


Hence, we know that, corresponding parts of the congruent triangles are equal


BD = CE


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