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Question
In triangle ABC, AB = AC; BE ⊥ AC and CF ⊥ AB.
Prove that:
(i) BE = CF
(ii) AF = AE
Solution
(i)
In ΔAEB and ΔAFC,
∠A = ∠A .......[Common]
∠AEB = ∠AFC = 90° ......[Given: BE ⊥ AC]
......[Given: 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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