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| 1) ABCD is a square. | 1) Given |
| 2) AD = BC | 2) Properties of square. |
| 3) ∠BAD = ∠ABC | 3) Each 900 and by properties of square. |
| 4) AB = BA | 4) Reflexive (common side) |
| 5) Δ ADB ≅ ΔBCA | 5) SAS postulate |
| 6) AC = BD | 6) CPCTC |
| 7) OB = OD | 7) As square is a parallelogram so diagonals of parallelogram bisect each other. |
| 8) AB = AD | 8) Properties of square. |
| 9) AO = AO | 9) Reflexive (common side) |
| 10) ΔAOB ≅ ΔAOD | 10) SSS Postulate |
| 11) ∠AOB = ∠AOD |
11) CPCTC |
| 12) ∠AOB + ∠AOD = 180 |
12) These two angles form linear pair and Linear pair angles are supplementary). |
| 13) 2∠AOB = 180 | 13) Addition property. |
| 14) ∠AOB = 90 | 14) Division property. |
| 15) AO ⊥ BD ⇒ AC ⊥ BD |
15) Definition of perpendicular. |
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| 1) ABCD is a parallelogram | 1) Given |
| 2) AC = BD and AC ⊥ BD | 2) Given |
| 3) AO = AO | 3) Reflexive |
| 4) ∠AOB = ∠AOD | 4) Each 900 |
| 5) OB = OD | 5) Properties of parallelogram. |
| 6) ΔAOB ≅ ΔAOD | 6) SAS Postulate |
| 7) AB = AD | 7) CPCTC |
| 8) AB = CD and AD = BC |
8) Properties of parallelogram. |
| 9) AB = BC = CD = AD | 9) From above |
| 10) AB = AB | 10) Reflexive (common side) |
| 11) AD = BC | 11) Properties of parallelogram. |
| 12) AC = BD | 12) Given |
| 13) ΔABD ≅ Δ BAC | 13) SSS Postulate |
| 14) ∠DAB = ∠CBA | 14) CPCTC |
| 15)∠DAB + ∠CBA = 180 | 15) Interior angles on the same side of the transversal. |
| 16) 2∠DAB = 180 | 16) Addition property |
| 17) ∠DAB = ∠CBA = 90 | 17) Division property |
