Lab Manual: Verify that the Parallelograms on the Same Base | Lab Manuals for Class 9 PDF Download

Objective

Materials Required
Graph paper, Two wooden strips, Nails, Elastic strings, A plywood piece, Adhesive

Prerequisite Knowledge
Concept of parallelogram & Area of a parallelogram

Theory

• Parallelogram: A quadrilateral in which both pairs of opposite sides are parallel, is called parallelogram and it is written as || gm.

In Fig. 20.1, ABCD is a parallelogram in which AB||CD and BO||AD.
Different properties of parallelograms are given below:

• A diagonal of a parallelogram divides it into two congruent triangles.
• In a parallelogram opposite angles are equal.
• In a parallelogram opposite sides are equal.
• Diagonals of a parallelogram bisect each other.

Procedure

• Take a rectangular plywood piece of suitable size and by using adhesive, paste a graph paper on it.
• Now, fix two horizontal wooden strips (parallel to each other) on it. (see Fig. 20.2)
• Fix two nails V₁ and V₂ on one of the strips, (see Fig. 20.2)
• On the other strip, fix nails at equal distances (B₁B₂ = B₂B₃ =… = B₈B₉). (see Fig. 20.2)
  Fig. 20.2

Demonstration

• We get a parallelogram V₁V₂B₈B₂ by putting a string along V₁V₂B₈ and B₂. We can find the area of parallelogram by counting the total number of squares.
• With same base V₁V₂ we get a parallelogram V₁V₂B₉B₃ by putting a string along V₁V₂B₉ and B₃. We can find the area of parallelogram by counting the total number of squares.
• We can conclude that area of parallelogram obtained in point 1, i.e. V₁V₂B₈B₂= area of parallelogram obtained in point 2, i.e. V₁V₂B₉B₃.

Observation
Total number of squares in 1 st parallelogram = …………. ,
Total number of squares in 2nd parallelogram = ………… ,
Total number of squares in 1 st parallelogram=Total number of squares in 2nd parallelogram Hence, area of 1st parallelogram = …………  of 2nd parallelogram

Result
We have verified that the parallelograms lying on the same base and between the same parallel lines are equal in area.

Application
The result is useful in

• many geometrical problems.
• deriving the formula for the area of a parallelogram.

Note: We can get the area of a parallelogram by counting squares.
For this, find the number of complete squares, half squares and more than half squares. Less than half squares may be ignored.