Construction of kite and trapezium — lesson. Mathematics CBSE, Class 8 New.

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Construction of a kite

Let us learn how to construct a kite when two diagonals are provided.

Example:

Construct a kite \(ABCD\) with diagonals \(AC = 10 \ cm\) and \(BD = 8 \ cm\).

Rough figure:

For kite \(ABCD\), diagonal \(AC\) bisects the diagonal \(BD\).

Thus, \(OB = OD = \frac{8}{2} = 4 \ cm\)

Also, the diagonals are perpendicular to each other.

\(\angle AOB = \angle BOC = \angle COD = \angle DOA = 90^{\circ}\)

Construction:

Step 1: Draw a line segment \(AC = 10 \ cm\).

Step 2: Mark a point \(O\) anywhere on the line segment \(AC\) and draw a perpendicular line to \(AC\) passing through \(O\).

Step 3: With \(O\) as the centre and \(4 \ cm\) as the radius, draw two arcs on the perpendicular line that intersect at \(B\) and \(D\).

Step 4: Join \(AB\), \(BC\), \(CD\) and \(DA\).

Thus, \(ABCD\) is the required kite.

Construction of an isosceles trapezium

Let us learn how to construct an isosceles trapezium in which the non-parallel sides are equal in length.

Example:

Construct an isosceles trapezium \(ABCD\) with \(AB \parallel CD\) and \(AB = 7 \ cm\) and \(AD = BC = 5 \ cm\).

Rough diagram:

Construction:

Step 1: Draw a line segment \(AB = 7 \ cm\).

Step 2: Draw a horizontal line parallel to \(AB\).

Step 3: With \(A\) and \(B\) as centres and a radius of \(5 \ cm\), draw an arc that cuts the horizontal line at \(D\) and \(C\), respectively.

Step 4: Join \(AD\) and \(BC\).

Thus, \(ABCD\) is the required isosceles trapezium.

Did you find an error?

8. Construction of kite and trapezium