MHB Euclidean Geometry - Demonstration Exercise

Samuel Gomes
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(a) Let be m a line and
[IMG]
the only two semiplans determined by m.

(i) Show that: If
[IMG]
are points that do not belong to
[IMG]
such
[IMG]
, so
[IMG]
and
[IMG]
are in opposite sides of m.

(ii) In the same conditions of the last item, show:
[IMG]
and
[IMG]
.

(iii) Determine the union result
[IMG]
, carefully justifying your answer.

(b) Let be
[IMG]
and
[IMG]
4 distincts points in a line
[IMG]
such
[IMG]
and
[IMG]
. Show
[IMG]
and
[IMG]
.

(c) Let be
[IMG]
distincts points in a line m such
[IMG]
. Under these conditions, show 2 distinct segments such the Union of both segments be equal to
[IMG]
, carefully justifying your answer.

Thanks for the help ^^
 
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