**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 V
_{1 }and V_{2}on one of the strips, (see Fig. 20.2) - On the other strip, fix nails at equal distances (B
_{1}B_{2}= B_{2}B_{3}=… = B_{8}B_{9}). (see Fig. 20.2)

**Demonstration**

- We get a parallelogram V
_{1}V_{2}B_{8}B_{2}by putting a string along V_{1}V_{2}B_{8 }and B_{2}. We can find the area of parallelogram by counting the total number of squares. - With same base V
_{1}V_{2 }we get a parallelogram V_{1}V_{2}B_{9}B_{3}by putting a string along V_{1}V_{2}B_{9 }and B_{3}. 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. V
_{1}V_{2}B_{8}B_{2}= area of parallelogram obtained in point 2, i.e. V_{1}V_{2}B_{9}B_{3}.

**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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