Class 9 Exam > Class 9 Notes > Lab Manual: Verify that the Parallelograms on the Same Base
Lab Manual: Verify that the Parallelograms on the Same Base - Class 9 PDF Download
Objective
To verify experimentally that the parallelograms on the same base and between same parallel lines are equal I in area.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.
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About this Document
Apr 23, 2025
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