Q2 of 45 Page 49

ΔABC is isosceles in which AB = AC. seg BD and seg CE are medians. Show that BD = CE.


Given: ΔABC is an isosceles triangle.


BD and CE are medians.


AB = AC


1/2 AB = 1/2 AC


Since, 1/2 AB = BE = AE and 1/2 AC = AD = CD


So, BE = CD ………….(1)


Also, ∠ABC = ∠ACB


⇒ ∠EBC = ∠DCB ……….(2)


In ΔEBC and ΔDCB


BE = CD [from (1)]


∠EBC = ∠DCB [from (2)]


BC = CB [common side]


∴ By SAS congruency


ΔEBC ≅ ΔDCB


So,


CE = BD …………..corresponding sides of congruent triangles.


∴ BD = CE


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