Class 09 To verify experimentally that in a triangle, the longer side has the greater angle opposite to it.

 

Activity 18

 OBJECTIVE                                                                    

To verify experimentally that in a triangle, the longer side has the greater angle opposite to it.

MATERIAL REQUIRED

 Coloured paper, scissors, tracing paper, geometry box, cardboard sheet, sketch pens.

 METHOD OF CONSTRUCTION

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

 2.   Cut out a ΔABC from a coloured paper and paste it on the cardboard [see Fig. 1].

 3.   Measure the lengths of the sides of ΔABC.

 4.   Colour all the angles of the triangle ABC as shown in Fig. 2.

 5.   Make the cut-out of the angle opposite to the longest side using a tracing paper [see Fig. 3].

DEMONSTRATION

 Take the cut-out angle and compare it with other two angles as shown in Fig. 4.

 ∠A is greater than both ∠B and ∠C.

 i.e., the angle opposite the longer side is greater than the angle opposite the other side.

 OBSERVATION

 Length of side AB = .......................

 Length of side BC = .......................

 Length of side CA = .......................

 Measure of the angle opposite to longest side = .......................

 Measure of the other two angles = ...................... and .......................

 The angle opposite the ...................... side is ...................... than either of the other

 two angles.

 APPLICATION

 The result may be used in solving different geometrical problems.

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.

Class 09 To verify exterior angle property of a triangle.

 Activity 16

 OBJECTIVE                                                                   

To verify exterior angle property of a triangle.

 METHOD OF CONSTRUCTION

  MATERIAL REQUIRED

Hardboard sheet, adhesive, glazed papers, sketch pens/pencils, drawing sheet, geometry box, tracing paper, cutter, etc.

1.   Take a hardboard sheet of a convenient size and paste a white paper on it.

 2.   Cut out a triangle from a drawing sheet/glazed paper and name it as ΔABC and paste it on the hardboard, as shown in Fig. 1.

 Produce the side BC of the triangle to a point D as shown in Fig. 2.

 4.   Cut out the angles from the drawing sheet equal to ∠A and ∠B using a tracing paper [see Fig. 3].

 5.   Arrange the two cutout angles as shown in Fig. 4.

 Fig. 3

 Fig. 4

 DEMONSTRATION

 ∠ACD is an exterior angle.

 ∠A and ∠B are its two interior opposite angles.

 ∠A and ∠B in Fig. 4 are adjacent angles.

 From the Fig. 4, ∠ACD = ∠A + ∠B.

 OBSERVATION

 Measure    of    ∠A=  __________,  Measure  of  ∠B  =  __________,

Sum (∠A + ∠B) = ________, Measure of ∠ACD = _______.

 Therefore, ∠ACD = ∠A + ∠B.

 APPLICATION

 This property is useful in solving many geometrical problems.

Class 09 To verify that the sum of the angles of a triangle is 180º.

 Activity 15

  OBJECTIVE                                                                    

To verify that the sum of the angles of a triangle is 180º.

 METHOD OF CONSTRUCTION

 MATERIAL REQUIRED

Hardboard sheet, glazed papers, sketch pens/pencils, adhesive, cutter, tracing paper, drawing sheet, geometry box.

 1.   Take a hardboard sheet of a convenient size and paste a white paper on it.

 2.   Cut out a triangle from a drawing sheet, and paste it on the hardboard and name it as ΔABC.

 3.   Mark its three angles as shown in Fig. 1

 Cut out the angles respectively equal to ∠A, ∠B and ∠C from a drawing sheet using tracing paper [see Fig. 2].

5.   Draw a line on the hardboard and arrange the cut-outs of three angles at a point O as shown in Fig. 3.

 Fig. 3

 DEMONSTRATION

 The three cut-outs of the three angles A, B and C placed adjacent to each other at a point form a line forming a straight angle = 180°. It shows that sum of the three angles of a triangle is 180º. Therefore, ∠A + ∠B + ∠C = 180°.

 OBSERVATION

 Measure of ∠A = -------------------.

 Measure of ∠B = -------------------.

 Measure of ∠C = -------------------.

 Sum (∠A + ∠B + ∠C) = -------------------.

 APPLICATION

 This result may be used in a number of geometrical problems such as to find the sum of the angles of a quadrilateral, pentagon, etc