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Question
In triangle ABC, AB = AC; BE ⊥ AC and CF ⊥ AB.
Prove that:
- BE = CF
- AF = AE
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Solution
(i)
In ΔAEB and ΔAFC,
∠A = ∠A ...[Common]
∠AEB = ∠AFC = 90° ...[Given: BE ⊥ AC and CF ⊥ AB]
AB = AC ...[Given]
⇒ ΔAEB ≅ AFC ...[AAS]
∴ BE = CF ...[C.p.c.t]
(ii) Since ΔAEB ≅ AFC
∠ABE = ∠AFC
∴ AF = AE ...[Congruent angles of congruent triangles]
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