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Question
ΔABC is isosceles in which AB = AC. Seg BD and seg CE are medians. Show that BD = CE.
Solution
Point D is the midpoint of line AC.
∴ AD = DC = `1/2` AC ...(1)
AE = EB = `1/2`AB ...(2)
AB = AC
Multiplying both sides by `1/2`
`1/2 "AB" = 1/2 "AC"` ...(3)
∴ AE = AD ...[(1), (2) and (3)] ...(4)
In, ΔBAD and ΔCAE
seg AB ≅ seg AC ...(Given)
∠BAD ≅ ∠CAE ...(Common side)
seg AE ≅ seg AD ...(From 4)
∴ ΔBAD ≅ ΔCAE ...(Congruence of SAS test)
∴ seg BD ≅ seg CE
∴ BD = CE
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