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Question
In the following figure, AB = AC and AD is perpendicular to BC. BE bisects angle B and EF is perpendicular to AB.
Prove that: BD = CD
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Solution
In ΔADB and ΔADC,
∠ADB = ∠ADC ...(Since AD is perpendicular to BC)
AB = AC ...(given)
AD = AD ...(common side)
∴ ΔADB ≅ ΔADC ...(RHS congruence criterion)
⇒ BD = CD ...(cpct)
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