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# Indirect Proof

Prove that $$\angle$$BDA is not a straight angle.
 Statement Reason 1) $$\angle$$BDA is a straight angle 1) (Assumpe opposite \) 2) m$$\angle$$BDA = 180° 2) Definition of a striaght angle 3)AD $$\perp$$ BC 3) Given 4) $$\angle$$BDA is a right angle 4) definition of perpendicular lines 5) m $$\angle$$BDA = 90° 5) definition of a right angle 6) m $$\angle$$BDA is not a straight angle contradiction of steps 2 and 5 7 $$\angle$$BDA is not a straight angle due to the contradiction between 2 and 5, we know that the assumption that WE INTRODUCED in the first step ($$\angle$$bda is a straight angle) is false. Therefore, the opposite must be true: $$\angle$$ is not a straight angle