Class 09 To verify experimentally that the sum of the angles of a quadrilateral is 360º.

 Activity 17

  OBJECTIVE                                                                  

To verify experimentally that the sum of the angles of a quadrilateral is 360º.

  METHOD OF CONSTRUCTION

   MATERIAL REQUIRED

 

Cardboard, white paper, coloured drawing sheet, cutter, adhesive, geometry box, sketch pens, tracing paper.

 1.   Take a rectangular cardboard piece of a convenient size and paste a white paper on it.

 2.   Cut out a quadrilateral ABCD from a drawing sheet and paste it on the cardboard [see Fig. 1].

 Make cut-outs of all the four angles of the quadrilateral with the help of a tracing paper [see Fig. 2]

4. Arrange the four cut-out angles at a point O as shown in Fig. 3.

 DEMONSTRATION

 1.   The vertex of each cut-out angle coincides at the point O.

2. Such arrangement of cut-outs

 shows that the sum of the angles

 of a quadrilateral forms a

 complete angle and hence is

equal to 360º.

 

OBSERVATION				Fig. 3
Measure of	∠A =	----------.
Measure of	∠B =	----------.	Measure of  ∠C =	----------.
Measure of	∠D =	----------.	Sum [ ∠A+ ∠B+ ∠C+ ∠D] =		-------------.

 APPLICATION

 This property can be used in solving problems relating to special types of quadrilaterals, such as trapeziums, parallelograms, rhombuses, etc.