Given : A triangle ABC. To Prove:∠A + ∠B + ∠C= 180^{0} Construction: Draw CE such that CE || AB |
1)BA || CE | 1) By Construction |
2) ∠A = ∠ACE | 2) Alternate interior angle |
3) ∠B = ∠DCE | 3) Corresponding angles |
4)∠A + ∠B = ∠ACE + ∠DCE | 4) Addition property of (1) and (2) |
5) ∠A + ∠B + ∠ACB = ∠ACE + ∠DCE + ∠ACB | 5) Adding ∠ACB to both sides |
6) ∠A + ∠B + ∠C = 180^{0} | 6) Straight line angles. |