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Question
A triangle ABC has ∠B = ∠C.
Prove that: The perpendiculars from B and C to the opposite sides are equal.
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Solution
Given: A ΔABC in which ∠B = ∠C.
BP is perpendicular from D to AC
CQ is the perpendicular from C to AB
We need to prove that
BP = CQ
Proof:
In ΔBPC and ΔCQB
∠B = ∠C ...[Given]
∠BPC = ∠CQB = 90 ...[BP AC and CQ AB]
BC = BC ...[Common]
∴ BY Angel-Angel-Side criterion of congruence,
ΔBPC ≅ ΔCQB
The corresponding parts of the congruent triangles are congruent.
BP = CQ ...[c.p.c.t]
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