Axiom 1. If L is a line, then there exist at least two points belonging to L. Ax

ID: 3028423 • Letter: A

Question

Axiom 1. If L is a line, then there exist at least two points belonging to L.

Axiom 2. If L is a line, then there exists at least one point that is not on L.

Axiom 3. There exists at least one line.

Axiom 4. If A and B are different points, then there exists only one line that contains both A and B.

Axiom 5. If ABC, then A, B, and C are three different points of some line and CBA.

Axiom 6. If A, B, and C are three different points of a line, then only one of the following holds: ABC, BCA, CAB.

Axiom 7. If A, B, C and D are four different collinear points and ABC, then only one of the following is true: ABCD, ABDC, ADBC, DABC.

Definition . ABCD means that ABC, ABD, ACD, and BCD.

1) Suppose ABC and ACD. Prove that ABD and BCD.

2)Suppose ABD and BCD. Prove that ABC and ACD.

1) Given that ABC and ACD

i.e. Points A, B and C is on the line and Points A ,C and D are on the lines

Since point A and Care common pont

Hence point B lies in between A and C and point D lies after point C

Hence configuration of point is A B C D

Hence ABD and BCD

Given that ABD and BCD

i.e. Points A, B and D is on the line and Points B,C and D are on the lines

Since point B and D are common pont

Hence point D lies in after A and B and point C lies in between B and D

Hence configuration of point is A B C D

Hence ABC and ACD

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