# UNIT 06: POLYGONS

## 1. SQUARE WITH SIDE s = 5 cm.

STEPS:

1. Draw the given side s = 5 cm. and name its endpoints C y D, they are two vertices of our square.
2. Get the perpendicular line to the segment on its endpoints C and D.
3. Centering your compass on point C draw an arc whose radius is 5 cm, the side of the square we want to get.
4. Where previous arc intersects the perpendicular line that passes through point C, we will get A, another vertex of our square.
5. Do the same on point D, and where the arc intersects the perpendicular line we will get vertex B.
6. Joining A, B, C and D we will get the square solution of this exercise.

## 2. SQUARE WITH DIAGONAL d = 5.5 cm.

STEPS:

1. Draw the given diagonal d = 5.5 cm and name its endpoints A and C, these are two vertices of the square.
2. Get the line bisector of segment AC.
3. Once we get the midpoint of segment AC, draw a circle whose center is the midpoint of the segment AC and whose radious is the middle of this segment.
4. Where this circle intersects the line bisector we will get the two other vertices of the square B and D.
5. If we join A, B, C and D we will get the square solution of this exercise.

## 3. RECTANGLE WHOSE LONGER SIDES ARE L = 5 cm. AND SMALLER ARE l = 3.5 cm.

STEPS:

1. Draw one of the biggest sides of the rectangle L = 5 cm. and name its endpoints C and D, these are two vertices of the rectangle.
2. Get the perpendicular line to the segment on its endpoints C and D.
3. Draw an arc centering your compass on point C with radious 3.5 cm.
4. Do the same centering your compass on point D.
5. Where these two arcs intersect each perpendicular line we will get the other two vertices of the rectangle A and B.
6. If we join A, B, C and D we will get the square solution of this exercise.

## 4. RECTANGLE GIVEN ITS DIAGONAL d = 6.5 cm. AND ONE OF ITS SMALLER SIDES l = 3 cm.

STEPS:

1. Draw the given diagonal d = 6.5 cm. and name its enpoints C and B, botho of them are vertices of the rectangle.
2. Get the line bisector of segment CB.
3. Once we have got the midpoint of segment CB, we will draw a circle which center is that point and which radious is the middle of segment CB, so you need to open your compass to point C or B.
4. Centering your compass on point C and B draw two arcs which radious is the smaller side of the rectangle l = 3 cm.
5. Where that two arcs cross the previously drawn circle we will get the other two vertices of the rectangle A and D.
6. If we join A, B, C and D we will get the rectangle solution of this exercise.

## 5. RECTANGLE GIVEN ITS DIAGONAL d = 6,5 cm.  AND THE ANGLE BETWEEN ITS DIAGONALS IS 30º

STEPS:

1. Draw the given diagonal d = 6.5 cm. and name its enpoints A and D, botho of them are vertices of the rectangle.
2. Get the line bisector of segment AD.
3. Once we have got the midpoint of segment AD, we will draw a circle which center is that point and which radious is the middle of segment CB, so you need to open your compass to point A or D.
4. Draw a 30º angle whose vertex is the midpoint of the given diagonal.
5. Where this angle intersects the previously drawn circle we will get the other two vertices of the rectangle B and C.
6. If we join A, B, C and D we will get the rectangle solution of this exercise.

## 6. QUADRILATERAL KNOWN ITS SIDES AND ONE OF ITS DIAGONALS AB = 4.5 cm., BC = 3.5 cm., CD = 5 cm., DA = 3 cm., AC = 6.5 CM.

STEPS:

1. Draw the given diagonal AC.
2. Draw an arc centering your compass on point A which radious is segment AB = 4.5 cm.
3. Draw an arc centering your compass on point C which radious is segment BC = 3.5 cm.
4. Where these two arcs intersect we will get B, a vertex of the quadrilateral.
5. Draw an arc centering your compass on point A which radious is segment DA = 3 cm.
6. Draw an arc centering your compass on point C which radious is segment CD = 5 cm.
7. Where these two arcs intersect we will get D, a vertex of the quadrilateral.
8. If we join A, B, C and D we will get the quadrilateral solution of this exerciseUniendo A, B, C y D.