BD and CE are bisectors of ∠B and ∠C of an isosceles △ABC with AB=AC. Prove that BD=CE.
Open in App
Solution
Solution:
Given: AB=AC and BD and CE are the bisectors of ∠B and ∠C respectively
To prove : BD=CE
Proof : In △ABC, AB=AC ⇒∠B=∠C…(i) (Angles opposite to equal sides are equal) ⇒12∠B=1/2∠C ⇒∠DBC=∠ECB…(ii)
Now, in △DBC and △EBC, BC=BC(Common) ∠C=∠B[ from (i) ] ∠DBC=∠ECB[ from (ii) ] ∴△DBC≅EBC(by ASA axiom)