Regular Polygons

1- Equilateral triangle
It is every triangle that has three sides with the same length.
Constructing an equilateral triangle with side AB
- Select the [b]COMPASS tool (Window 8)[/b]. Then click on point [b]A [/b]and point[b] B[/b] (It represents the length opening of the compass) and again on point [b]A [/b](It represents the sharp end of the compass). Then click on [b]B [/b]and[b] A [/b](It represents the length opening of the compass) and again on [b]B[/b] (It represents the sharp end of the compass[b]).[br]note: you can click on the segment line to indicate the opening of the measure.[/b] [br][b]- [/b]Select the INTERSECT tool [b](Window 3)[/b] and mark a point [b]c[/b], point of intersection of the last two circles.  [br]- Select the [b]SEGMENT option (Window 5)[/b] and draw the line segments [b]BC [/b]and [b]AC[/b]. [br]- Select the [b]SHOW/HIDE OBJECT tool (Window 9)[/b] and hide the circles. [br]- Select the [b]MOVE tool (Window 1)[/b]  Move point [b]A[/b] or [b]B.[/b] What can you see? Is the triangle equilateral? Justify your answer.
2-Square
It is any quadrilateral that all 4 sides have the same length and that the internal angles all have the[br]same size.
Constructing a Square with side AB
- Select the [b]LINE[/b] [b]tool (Window 4)[/b]. Then click on [b]A [/b]and[b] B.[br][/b]- Select the [b]COMPASS tool (Window 8)[/b]. Then click on[b] A[/b] and [b]B [/b](It represents the length opening of[br]the compass) and again on [b]A[/b] (It represents the sharp end of the compass). [br][b]note: you can click on the segment line to indicate the length opening of the compass.[/b] [br][b]- [/b]Select the [b]INTERSECT (Window 3)[/b] and mark an intersection (on the left side) [b]C [/b]of the circle with the line. [br]- Select the [b]COMPASS tool (Window 8)[/b]. Then click on point [b] C [/b] and point [b]B[/b] (It represents the length opening of the compass) and again on point [b] C [/b](It represents the sharp end of the compass). After that click on point [b] B [/b] and point [b]C [/b](It represents the length opening of the compass) and again on [b]B[/b] (It represents the sharp end of the compas). [br][b]- [/b]Select the [b]INTERSECT tool (Window 3) [/b]and mark and intersection (on the upper side)[b] D[/b] between two circles.  [br]- Select the [b]SHOW / HIDE OBJECT tool (Window 9)[/b] and hide the circles. [br]- Select the [b]LINE[/b] [b]tool (Window 6)[/b]. Then click on [b]A [/b]and[b] D. [/b]This line is perpendicular to segment [b]AB. [/b] [br]- Select the [b]INTERSECT (Window 3)[/b] and mark an intersection (on the upper side) [b]E [/b]of the circle [b]c[/b] with the perpendicular.[br]- Select the [b]COMPASS tool (Window 8)[/b]. Then click on point [b]B [/b]and point[b] A[/b] (It represents the length opening of the compass) and again on point [b]B [/b](It represents the sharp end of the compass). [br][b]- [/b]Select the [b]INTERSECT (Window 3)[/b] and mark an intersection (on the right side) [b]F [/b]of the circle with the line.  [br]- Select the [b]COMPASS tool (Window 8)[/b]. Then click on point [b]F [/b]and point [b]A [/b](It represents the length opening of the compass) and again on point [b]F [/b](It represents the sharp end of the compass). After that, click on point [b]A [/b]and point[b] F[/b] (It represents the length opening of the compass) and again on [b]A[/b] (It represents the sharp end of the compass). [br][b]- [/b]Select the [b]INTERSECT tool (Window 3)[/b] and mark [b]G [/b]as an intersection (on the upper side) between the last two circçes.[br]- Select the [b]SHOW/HIDE OBJECT tool (Window 9)[/b] and hide the last two cirunferences. [br]- Select the LINE [b]tool (Window 4)[/b]. Then click on [b]B [/b]and[b] G. [/b]This line is perpendicular to segment [b]AB. [/b] [br]- Select the [b]INTERSECT[/b] [b]tool (Window 3)[/b] and mark an intersection (on the upper side) [b]H [/b]of the circle [b]k[/b] with the perpendicular.[br]- Select the [b]SEGMENT tool (Window 5)[/b] and draw the line segments [b]AE, EH [/b]e [b]HB[/b].[br]- Select the [b]SHOW/HIDE OBJECT tool (Window 9)[/b] and hide all objects, leaving only the square. [br]- Select the [b]MOVE tool (Window 1)[/b]  Move point [b]A[/b] or [b]B.[/b] What can you see? Is the quadrilateral a square? Justify your answer.
3-Regular Hexagon
It is any polygon with 6 sides that all sides have the same length and that the internal angles all have the[br]same size.
Constructing a regular hexagon with side AB
- Select the [b]COMPASS tool (Window 8)[/b]. Then click on line segment [b]AB[/b] (It represents the length opening of the compass) and on [b]A [/b](It represents the sharp end of the compass). Then click on segment [b]AB[/b] (opening of the compass) and on [b]B[/b] (dry end of the compass). [br][b]- [/b]Select the [b]INTERSECT[/b] [b]tool (Window 3)[/b] and mark an intersection (on the upper side) [b]C [/b]of the circles.  [br]- Select the [b]COMPASS tool (Window 8)[/b]. Then click on point[b] C [/b]and point[b] B[/b] (It represents the length opening of the compass) and again on [b] point C [/b](It represents the sharp end of the compass). [br][b]- [/b]Select the [b]INTERSECT (Window 3)[/b] and mark an intersection (on the left side) [b]D [/b]of the circle [b]e [/b]with the circle [b]c[/b]. Also mark an intersection (on the right side) [b]E[/b] of the [b]circles D[/b] [b]and [/b]E.  [br]- Select the [b]COMPASS tool (Window 8)[/b]. Then click on point [b]D [/b]and point[b] A[/b] (It represents the length opening of the compass) and again on point [b]D [/b](It represents the sharp end of the compass). After that, click on point [b]E [/b]and point[b] B[/b] (It represents the length opening of the compass) and again on [b]E[/b] (It represents the sharp end of the compass). [br][b]- [/b]Select the [b]INTERSECT[/b] [b]tool (Window 3)[/b] and mark an intersection (on the upper side) [b]F [/b]of the circle [b]and[/b] with the circle [b]g[/b]. Also mark a (on the upper side) intersection [b]G[/b] of the circles [b]h[/b] and [b]e[/b].  [br]- Select the [b]SEGMENT option (Window 5)[/b] and draw the segments [b]AD, DF, FG, GE [/b]and [b]BE[/b]. [br]- Select the [b]SHOW/HIDE OBJECT tool (Window 9)[/b] and hide all objects, leaving only the square. [br]- Select the [b]ANGLE tool (Window 10)[/b] and measure all internal angles. - Select the [b]MOVE tool[br](Window 1)[/b]  move point [b]A[/b] or [b]B.[/b]

Information: Regular Polygons