Construction of Rectangles

overview

In this page, constructing rectangles is explained. It is outlined as follows.

• Properties of rectangles is explained

• The number of independent parameters in a rectangle is 11

• For a given parameter, construction of rectangles is approached as combination of triangles (sss, sas, asa, rhs, sal) and using the properties of rectangles.

understanding rectangle

A rectangle is a parallelogram with all interior angles 90∘90∘

A quadrilateral is defined by 55 parameters. A Parallelogram is defined by 33 parameters. And for a rectangle, the following properties provide additional dependency of parameters.

• all interior angles are 90∘90∘

• diagonals are equal and bisect

• opposite sides are parallel and equal

• two angles on diagonals are supplementary.

These properties cause one parameter to be dependent on other parameters and so, *a rectangle is defined by 22 parameters*.

To construct a rectangle, 2 sides (¯AB, ¯BC) are given. This is illustrated in the figure. To construct, consider this as two SAS triangles ABC and ABD.

To construct a rectangle, a side (¯AB) and the diagonal (¯AC) are given. This is illustrated in the figure. To construct, consider this as two RHS triangles ABC and ABD.

To construct a rectangle, the diagonal (¯AC) and the angle between them (∠DOC) are given. This is illustrated in the figure.

To construct the specified rectangle, "Consider this as two SAS triangle COD and AOB". Note: Use the property that diagonals bisect and mark the vertices at half diagonals.

summary

**Construction of Rectangles** :

Properties of rectangle

• all interior angles are 90∘

• diagonals are equal and bisect

• opposite sides are parallel and equal

The formulations of questions

• 2 sides

• 1 side and the diagonal

• the diagonal and an angle between the diagonals
*use properties to figure out dependent parameters and look for triangles*

Outline

The outline of material to learn "Construction / Practical Geometry at 6-8th Grade level" is as follows.
Note: * click here for detailed outline of "constructions / practical geometry".*

• Four Fundamenatl elements

→ __Geometrical Instruments__

→ __Practical Geometry Fundamentals__

• Basic Shapes

→ __Copying Line and Circle__

• Basic Consustruction

→ __Construction of Perpendicular Bisector__

→ __Construction of Standard Angles__

→ __Construction of Triangles__

• Quadrilateral Forms

→ __Understanding Quadrilaterals__

→ __Construction of Quadrilaterals__

→ __Construction of Parallelograms__

→ __Construction of Rhombus__

→ __Construction of Trapezium__

→ __Construction of Kite__

→ __Construction of Rectangle__

→ __Construction of Square__