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प्रश्न
In triangles ABC and CDE, if AC = CE, BC = CD, ∠A = 60°, ∠C = 30° and ∠D = 90°. Are two triangles congruent?
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उत्तर
For the triangles ABC and ECD, we have the following information and corresponding figure:
AC = CE
BC = CD
∠A = 60°
∠C = 30°
∠D = 90°

In triangles ABC and ECD, we have
AC = EC
BC = CD
and ∠BAC= ∠CED
The SSA criteria for two triangles to be congruent are being followed. So both the triangles are congruent.
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संबंधित प्रश्न
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- BD = AC
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- ΔAMC ≅ ΔBMD
- ∠DBC is a right angle.
- ΔDBC ≅ ΔACB
- CM = `1/2` AB

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Given: EB = DB
AE = BC
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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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Prove that : ED = EF

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In ΔABC, AB = AC and the bisectors of angles B and C intersect at point O.
Prove that : (i) BO = CO
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