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Question
ABC is an isosceles triangle with AB = AC and BD and CE are its two medians. Show that BD = CE.
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Solution
Given: ABC is an isosceles triangle with AB = AC and BD and CE are its two medians.
To prove: BD = CE
Proof: In triangle ABC,
AB = AC ...[Given]
`1/2 AB = 1/2 AC`
AE = AD ...[D is the mid-point of AC and E is the mid-point of AB]
Now, in triangle ABD and triangle ACE,
AB = AC ...[Given]
∠A = ∠A ...[Common angle]
AE = AD ...[Above proved]
Now, by SAS criterion of congruence, we get
ΔABD ≅ ΔACE
BD = CE ...[CPCT]
Hence proved.
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