Q4 of 56 Page 119

In ΔABC points D and E are situated on sides AB and AC respectively such that BD = CE. If ∠B = ∠C then show that DE || BC.

In ΔABC & ΔADE


∠B = ∠C |Given


⇒ AC = AB |sides opposite to equal angles are equal


⇒ AB = AC …(1)


Given,


BD = CE


Subtracting BD from AB and CE from AC,


⇒ AB – BD = AC – CE


⇒ AD = AE |...(2)


In ΔABC & ΔADE,


From (1) and (2)



∠B = ∠C


⇒ ABC~ADE by SAS Similarity Rule


⇒ ∠ADE = ∠ABC


⇒ DE||BC as all corresponding angles are equal.


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