# Regular Polygons

- Author:
- Jorge Cássio

## 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.**