GeoGebra Classroom

# 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 COMPASS tool (Window 8). Then click on point A and point B (It represents the length opening of the compass) and again on point A (It represents the sharp end of the compass). Then click on B and A (It represents the length opening of the compass) and again on B (It represents the sharp end of the compass). note: you can click on the segment line to indicate the opening of the measure. - Select the INTERSECT tool (Window 3) and mark a point c, point of intersection of the last two circles.   - Select the SEGMENT option (Window 5) and draw the line segments BC and AC. - Select the SHOW/HIDE OBJECT tool (Window 9) and hide the circles. - Select the MOVE tool (Window 1)  Move point A or 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 same size.

## Constructing a Square with side AB

- Select the LINE tool (Window 4). Then click on A and B. - Select the COMPASS tool (Window 8). Then click on A and B (It represents the length opening of the compass) and again on A (It represents the sharp end of the compass). note: you can click on the segment line to indicate the length opening of the compass. - Select the INTERSECT (Window 3) and mark an intersection (on the left side) C of the circle with the line. - Select the COMPASS tool (Window 8). Then click on point  C  and point B (It represents the length opening of the compass) and again on point  C (It represents the sharp end of the compass). After that click on point  B  and point C (It represents the length opening of the compass) and again on B (It represents the sharp end of the compas). - Select the INTERSECT tool (Window 3) and mark and intersection (on the upper side) D between two circles.   - Select the SHOW / HIDE OBJECT tool (Window 9) and hide the circles. - Select the LINE tool (Window 6). Then click on A and D. This line is perpendicular to segment AB.   - Select the INTERSECT (Window 3) and mark an intersection (on the upper side) E of the circle c with the perpendicular. - Select the COMPASS tool (Window 8). Then click on point B and point A (It represents the length opening of the compass) and again on point B (It represents the sharp end of the compass). - Select the INTERSECT (Window 3) and mark an intersection (on the right side) F of the circle with the line.   - Select the COMPASS tool (Window 8). Then click on point F and point A (It represents the length opening of the compass) and again on point F (It represents the sharp end of the compass). After that, click on point A and point F (It represents the length opening of the compass) and again on A (It represents the sharp end of the compass). - Select the INTERSECT tool (Window 3) and mark G as an intersection (on the upper side) between the last two circçes. - Select the SHOW/HIDE OBJECT tool (Window 9) and hide the last two cirunferences. - Select the LINE tool (Window 4). Then click on B and G. This line is perpendicular to segment AB.   - Select the INTERSECT tool (Window 3) and mark an intersection (on the upper side) H of the circle k with the perpendicular. - Select the SEGMENT tool (Window 5) and draw the line segments AE, EH e HB. - Select the SHOW/HIDE OBJECT tool (Window 9) and hide all objects, leaving only the square. - Select the MOVE tool (Window 1)  Move point A or 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 same size.

## Constructing a regular hexagon with side AB

- Select the COMPASS tool (Window 8). Then click on line segment AB (It represents the length opening of the compass) and on A (It represents the sharp end of the compass). Then click on segment AB (opening of the compass) and on B (dry end of the compass). - Select the INTERSECT tool (Window 3) and mark an intersection (on the upper side) C of the circles.   - Select the COMPASS tool (Window 8). Then click on point C and point B (It represents the length opening of the compass) and again on  point C (It represents the sharp end of the compass). - Select the INTERSECT (Window 3) and mark an intersection (on the left side) D of the circle e with the circle c. Also mark an intersection (on the right side) E of the circles D and E.   - Select the COMPASS tool (Window 8). Then click on point D and point A (It represents the length opening of the compass) and again on point D (It represents the sharp end of the compass). After that, click on point E and point B (It represents the length opening of the compass) and again on E (It represents the sharp end of the compass). - Select the INTERSECT tool (Window 3) and mark an intersection (on the upper side) F of the circle and with the circle g. Also mark a (on the upper side) intersection G of the circles h and e.   - Select the SEGMENT option (Window 5) and draw the segments AD, DF, FG, GE and BE. - Select the SHOW/HIDE OBJECT tool (Window 9) and hide all objects, leaving only the square. - Select the ANGLE tool (Window 10) and measure all internal angles. - Select the MOVE tool (Window 1)  move point A or B.