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If lines AB,AC,AD and AE are parallel to a line l show that points A,B,C,D and E are collinear.

Answer»

Solution :Given : LINE AB, AC, AD and AE are parallel to a line l.
To prove : A, B, C, D, E are collinear.
PROOF : Since AB, AC, AD, AE are all parallel to a line l, it follows that A is a point outside l, through which lines AB,AC,AD and AE are drawn, each parallel to l.
But by parallel lines AXIOMS one and only one line can be drawn through A and parallel to l.
This is possible only when A,B,C,D,E all lie on the same line.
Hence, A,B,C,D,E are collinear.


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