If lines AB, AC, AD and AE are parallel to a line $l$ , what can be said about the points A, B, C, D and E?

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Solution

By Parallel Playfair's Axiom, if 'l' is a line and a point P not on it, there is one and only one line 'm' which passes through P and is parallel to 'l'. Here, AB, AC, AD, AE are the lines through the point A parallel to the line 'l'. The points A, B, C, D, E all lie on the line m. Hence the points A, B, C, D, E are collinear.

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If lines AB, AC, AD and AE are parallel to a line l, what can be said about the points A, B, C, D and E?

If lines AB, AC, AD and AE are parallel to a line $l$ , what can be said about the points A, B, C, D and E?