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Question
In ∆ABC, AB = AC. Show that the altitude AD is median also.
Solution
In ∆ABD and ∆ADC,
AB = AC ...(Since is an isosceles triangle)
AD = AD ...(common side)
∠ADB = ∠ADC ...(Since AD is the altitude so each is 90°)
⇒ ΔADB ≅ ΔADC ...(RHS congruence criterion)
BD = DC ...(cpct)
⇒ AD is the median.
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