firmfunda
  maths > construction-basics

Construction of Kite


    what you'll learn...

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.

kite construction introduction

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 360360

A kite is defined by 33 parameters.

construction of kite with 2 unequal sides, angle

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

construction of kite with 1 side, and 2 angles

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.

construction of kite with 2 unequal sides, major diagonal

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

construction of kite with 2 unequal sides, minor diagonal

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

construction of kite with 1 side, major diagonal, angle between them

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

kite construction introduction

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