Construction of Quadrilaterals

overview

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

• Properties of quadrilaterals is explained

• The number of independent parameters in a quadrilateral is $1$

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

recap

In a quadrilateral,

• sum of all interior angles is $360}^{\circ$.
A quadrilateral is made of two triangles sharing one side. Each triangle is defined by $3$ parameters and since they share a side, one parameter is common in the two sets of $3$ parameters. Thus, a quadrilateral is defined by $5$ parameters.

To construct a quadrilateral, 4 sides ($\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{AD}$ ) and a diagonal ($\overline{AC}$) are given. This is illustrated in the figure. The quadrilateral can be constructed by considering this as two SSS triangles $ABC$ and $ACD$

To construct a quadrilateral, 4 ($\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{AD}$ ) sides and an angle ($\angle B$) are given. This is illustrated in the figure. The quadrilateral can be constructed by considering this as an SAS triangle $ABC$ and another SSS triangle $ACD$

To construct a quadrilateral, $3$ ($\overline{AB}$, $\overline{BC}$, $\overline{AD}$ ) sides and two diagonals ($\overline{AC}$, $\overline{BD}$) are given. This is illustrated in the figure. The quadrilateral can be constructed by considering consider this as two SSS triangles $ABC$ and $ABD$

To construct a quadrilateral, $3$ sides ($\overline{AB}$, $\overline{BC}$, $\overline{AD}$ ) and $2$ angles ($\angle A$, $\angle B$) are given. This is illustrated in the figure. The quadrilateral can be constructed by considering this as two SAS triangles $ABC$ and $BAD$.

To construct a quadrilateral, $2$ sides ($\overline{AB}$, $\overline{BC}$ ) and $3$ angles ($\angle A$, $\angle B$, $\angle C$)are given. This is illustrated in the figure. To construct, "consider this as an SAS triangle $ABC$ and another ASA triangle with two angles $\angle C$ and $\angle A$". Note that $\u25b3ACD$ is formed by angles $\angle C$ and $\angle A$

summary

**Construction of Quadrilateral** : Properties of quadrilaterals

• sum of interior angles $360}^{\circ$

The formulations of questions

• 4 sides and a diagonal

• 3 sided and 2 diagonals

• 4 sides and an angle

• 3 sides and 2 angles

• 2 sides and 3 angles

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__