NCERT Class 9 Maths Lab Manual – Verify that the Parallelograms on the Same Base
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.
- For area of parallelogram refer to Activity 19.
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)
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.
Viva Voce
Question 1:
What is the relationship between the areas of the parallelograms on the same base (or equal bases) and between the same parallel lines?
Answer:
Both areas are same.
Question 2:
What are the types of parallelogram?
Answer:
Parallelograms are of three types, Le. rectangle, square and rhombus.
Question 3:
How would you define the area of a parallelogram?
Answer:
Area of parallelogram Is the product of its base and the corresponding altitude.
Question 4:
What is the altitude of a parallelogram?
Answer:
Altitude of parallelogram is perpendicular distance between two parallel sides.
Question 5:
Does the diagonals of a parallelogram divide it into two triangles of equal base?
Answer:
No, the diagonals of a parallelogram divide it into four triangles of equal base.
Question 6:
Is it correct that every square and rhombus are parallelogram?
Answer:
Yes, because opposite sides of there figures are parallel and equal.
Question 7:
In which quadrilateral figure diagonals are not equal other than parallelogram?
Answer:
Rhombus
Question 8:
Is it correct that the diagonals of a parallelogram bisects the angles?
Answer:
Yes
Suggested Activity
Using the above activity, find the area of an isosceles trapezium, if one of its non-parallel side is 5 cm and lengths of two parallel sides are 4 cm and 10 cm.
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