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Question
A triangle ABC has ∠B = ∠C.
Prove that: The perpendiculars from the mid-point of BC to AB and AC are equal.
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Solution
Given: A ΔABC in which ∠B = ∠C.
DL is the perpendicular from D to AB
DM is the perpendicular from D to AC
We need to prove that
DL = DM
Proof:
In ΔDLB and ΔDMC
∠DLB = ∠DMC=900 ...[ DL ⊥ AB and DM ⊥ AC ]
∠B=∠C ...[ Given ]
BD= DC ...[ D is the midpoint of BC ]
∴ By Angel-Angel-SIde Criterion of congruence,
ΔDLB ≅ ΔDMC
The corresponding parts of the congruent triangles are congruent.
∴DL=DM ...[ c.p.c.t ]
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