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प्रश्न
A triangle ABC has ∠B = ∠C.
Prove that: The perpendiculars from B and C to the opposite sides are equal.
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उत्तर
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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संबंधित प्रश्न
AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠BAD = ∠ABE and ∠EPA = ∠DPB (See the given figure). Show that
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You have to show that ΔAMP ≅ AMQ.
In the following proof, supply the missing reasons.
| Steps | Reasons | ||
| 1 | PM = QM | 1 | ... |
| 2 | ∠PMA = ∠QMA | 2 | ... |
| 3 | AM = AM | 3 | ... |
| 4 | ΔAMP ≅ ΔAMQ | 4 | ... |
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