Suppose ABA? holds(B is between A and A') and D ? Int(?ABC). Prove that C ? Int(?A?BD). (a)...

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Suppose ABA? holds(B is between A and A') and D ?Int(?ABC). Prove that C ? Int(?A?BD).
(a) Prove that C ? H(D,line A?B).
(b) Prove that C ? H (A?, line??BD). Use point A.
(c) Deduce that C?Int (?A?BD).

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a If A and D are points on the same side of a line BC and the line BA is parallel to the line CD then m ABC m BCD 180 To obtain a contradiction suppose that CD then m ABC m BCD 6 180 Case 1 Suppose m ABC m BCD 180 Then applying Euclids 5th Postulate the lines BA and CD meet at a point P on the same side of BC as A and D But BA and CD are parallel so this is a contradiction Case 2 Suppose m ABC m BCD 180 Let E be a point on AB such that A B E Similarly See Answer

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