Class 09 To verify that the triangles on the same base and between the same parallels are equal in area.

 

Activity 20

 OBJECTIVE                                                                 

To verify that the triangles on the same base and between the same parallels are equal in area.

 MATERIAL REQUIRED

A piece of plywood, graph paper, pair of wooden strips, colour box , scissors, cutter, adhesive, geometry ox.

METHOD OF CONSTRUCTION

1.   Cut a rectangular plywood of a convenient size.

 2.   Paste a graph paper on it.

 3.   Fix any two horizontal wooden strips on it which are parallel to each other.

4.   Fix two points A and B on the paper along the first strip (base strip).

5.   Fix a pin at a point, say at C, on the second strip.

6.   Join C to A and B as shown in Fig. 1.

7.   Take any other two points on the second strip say C^′ and C^′′ [see Fig. 2].

 8.   Join C^′A, C^′B, C^′′A and C^′′B to form two more triangles.

DEMONSTRATION

 1. Count the number of squares contained in each of the above triangles, taking

 1 half square as ₂ and more than half as 1 square, leaving those squares which1

contain less than       squares.

 2.    See that the area of all these triangles is the same. This shows that triangles on the same base and between the same parallels are equal in area.

 OBSERVATION

 1.   The number of squares in triangle ABC =.........., Area of ΔABC = ........ units

 2.   The number of squares in triangle ABC^′ =......., Area of D ABC^′ = ........ units

 3.   The number of squares in triangle ABC^′′ =....... , Area of D ABC^′′ = ........ units Therefore, area (ΔABC) = ar(ABC^′) = ar(ABC^′′).

 APPLICATION

 This result helps in solving various geometric problems. It also helps in finding the formula for area of a triangle. 

Fig. 1