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**OReilly** I have to prove that if A-B-C and A-D-C, then A,B,C,D are points of one line and it isn't B-A-D.

I see that B and D are on same side based on A-B-C and A-D-C, so it couldn't be B-A-D.

Solution from book goes: If we assume that B-A-D is true then B and D are on different sides of A, so based on A-B-C it will be A-C-D which is false.

I don't understand why solution from book says that based on B-A-D and A-B-C it must be A-C-D?

Isn't that based on B-A-D and A-B-C must be D-A-C?