Construction of Kite

overview

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

• Properties of kites is explained

• The number of independent parameters in a kite is 11

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

Understanding Kite

A kite is a quadrilateral with two pair of equal and adjacent sides.

A quadrilateral is defined by 55 parameters. For a kite, the following properties provide additional dependency of parameters

• two pair of equal sides

• major diagonal perpendicularly bisects the minor diagonal. *the diagonal that divides the kite into two congruent triangles is called major. The other diagonal is the minor diagonal.*

• major diagonal bisects the angles at the vertices

• two equal opposite angles and two unequal opposite angles -- all sum up to 360∘360∘*A kite is defined by 33 parameters*.

To construct a kite, 22 unequal sides (¯AB¯¯¯¯¯¯AB, ¯BC) and the angle between them (∠B) are given. This is illustrated in the figure. To construct, consider this as an SAS triangle in BAD and SSS triangle BCD

To construct a kite, a side (¯AB) and 2 angles (∠A,∠B) are given. This is illustrated in the figure. To construct, consider as an SAS triangle in ABC and ASA triangle ACD.

To construct a kite, 2 unequal sides (¯AB, ¯BC) and the major diagonal (¯BD) are given. This is illustrated in the figure. To construct, consider as two SSS triangles in ABD and BDC

To construct a kite, 2 unequal sides (¯AB, ¯BC) and the minor diagonal (¯AC) are given. This is illustrated in the figure. To construct, consider as two isosceles SSS triangles in ABC and ACD

To construct a kite, a side (¯AB), the major diagonal (¯BD), and angle (∠ABD) between them are given. This is illustrated in the figure. To construct, consider this as two SAS triangles in ABD and DBC

summary

**Construction of Kite** :

Properties of Kite:

• two pair of equal sides

• major diagonal perpendicularly bisects the minor diagonal. *The diagonal that divides the kite as two congruent triangles is the major diagonal.*

• major diagonal bisects the angles at the vertices

• two equal opposite angles and two unequal opposite angles sum up to 360∘

The formulations of questions

• 2 unequal sides and the angle between them

• 1 side and 2 angles

• 2 unequal sides and the major diagonal

• 2 unequal sides and the minor diagonal

• 1 side, major diagonal and the angle between them

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__