Euclidean Geometry - Demonstration Exercise

[Samuel Gomes]

(a) Let be m a line and

the only two semiplans determined by m.

(i) Show that: If

are points that do not belong to

such

, so

and

are in opposite sides of m.

(ii) In the same conditions of the last item, show:

and

.

(iii) Determine the union result

, carefully justifying your answer.

(b) Let be

and

4 distincts points in a line

such

and

. Show

and

.

(c) Let be

distincts points in a line m such

. Under these conditions, show 2 distinct segments such the Union of both segments be equal to

, carefully justifying your answer.

Thanks for the help ^^