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.
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OBSERVATION |
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Fig. 3 |
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Measure of |
∠A = |
----------. |
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Measure of |
∠B = |
----------. |
Measure
of ∠C = |
----------. |
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Measure of |
∠D = |
----------. |
Sum [ ∠A+ ∠B+ ∠C+ ∠D] = |
-------------. |
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APPLICATION
This property can be used in solving problems relating to special types of quadrilaterals, such as trapeziums, parallelograms, rhombuses, etc.
