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Angle angle side postulate (AAS)-> If two angles and a non-included side of a triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent by angle angle side postulate. |
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1) ∠B = ∠C | 1) Given |
2) ∠BAD = ∠CAD | 2) By construction |
3) AD = AD | 3) Reflexive (common side) |
4) ΔABD ≅ ΔACD | 4) By angle angle side postulate (AAS) |
5) AB = AC | 5) By CPCTC |
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1) AB = AC | 1) Given |
2) ∠ABC = ∠ACB | 2) If two sides are congruent then the angle opposite to them are also congruent |
3) ∠CEB = ∠BDC | 3) Each 900 |
4) BC = BC | 4) Reflexive (common side) |
5) ΔBCE ≅BCD | 5) By AAS postulate |
6) BD = CE | 6) CPCTC |
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1) ∠A = ∠C | 1) Given |
2) ∠AOE = ∠COD | 2) Vertically opposite angles |
3) ∠A + ∠AOE = ∠C + ∠COD | 3) Add (1) and (2) |
4) 1800 - ∠AEO = 1800 - ∠CDO | 4) Since ∠A + ∠AOE + ∠AEO = 180 and ∠C + ∠COD + ∠CDO = 180 |
5) ∠AEO = ∠CDO | 5) By subtraction property |
6) ∠AEO + ∠OEB = 1800 | 6) Linear pair angles |
7) ∠CDO + ∠ODB = 1800 | 7) Linear pair angles |
8) ∠AEO + ∠OEB = ∠CDO + ∠ODB | 8) Transitive property |
9) ∠OEB = ∠ODB | 9) Subtraction property and from(5) |
10) ∠CEB = ∠ADB | 10) Since ∠OEB = ∠CEB and ∠ODB = ∠ADB |
11) AB = BC | 11) Given |
11) ΔABD ≅ ΔCBE | 11) By AAS postulate (from (1),(10)) |