Euclidean Geometry - Demonstration Exercise

Discussion in 'Geometry and Trigonometry' started by Samuel Gomes, May 15, 2022.

  1. Samuel Gomes

    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 ^^
     
    Samuel Gomes, May 15, 2022
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