# UNIT 06: POLYGONS

## EXERCISE 07: QUADRILATERALS I

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

STEPS:

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

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

STEPS:

- Draw the given diagonal d = 5.5 cm and name its endpoints A and C, these are two vertices of the square.
- Get the line bisector of segment AC.
- 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.
- Where this circle intersects the line bisector we will get the two other vertices of the square B and D.
- 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:

- 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.
- Get the perpendicular line to the segment on its endpoints C and D.
- Draw an arc centering your compass on point C with radious 3.5 cm.
- Do the same centering your compass on point D.
- Where these two arcs intersect each perpendicular line we will get the other two vertices of the rectangle A and B.
- 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:

- Draw the given diagonal d = 6.5 cm. and name its enpoints C and B, botho of them are vertices of the rectangle.
- Get the line bisector of segment CB.
- 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.
- Centering your compass on point C and B draw two arcs which radious is the smaller side of the rectangle l = 3 cm.
- Where that two arcs cross the previously drawn circle we will get the other two vertices of the rectangle A and D.
- 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:

- Draw the given diagonal d = 6.5 cm. and name its enpoints A and D, botho of them are vertices of the rectangle.
- Get the line bisector of segment AD.
- 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.
- Draw a 30º angle whose vertex is the midpoint of the given diagonal.
- Where this angle intersects the previously drawn circle we will get the other two vertices of the rectangle B and C.
- 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:

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

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