**CBSE Class 9 Maths Lab Manual – Parallelogram**

**Objective**

To obtain a parallelogram by paper folding, whose adjacent sides are given.

**Prerequisite Knowledge**

- Parallelogram is a quadrilateral in which the pairs of opposite sides are equal and parallel.
- Basic properties of parallelogram.

**Materials Required**

Glazed papers, pen, pencil, scale.

**Procedure**

- Take a sheet of glazed paper. Draw any two intersecting rays AB and BC such that they form an acute angle which will be the two adjacent sides of a parallelogram.

- Fold the paper along a line that cuts the line BC, the part of line BC that lies on one side of the line of fold falls on the other part. Make a crease, such that X
_{1}Y_{1}⊥BC and unfold the paper.

- Fold the paper such that line passes through the point A and is parallel to BC. Make a crease and unfold the paper. Draw the dotted line X
_{2}Y_{2}.

- Fold the paper along the line that passes through the point C which is parallel to the line AB and cuts the line X
_{2}Y_{2}. Make a crease and unfold it. Draw the line X_{3}Y_{3}parallel to AB. Mark the intersecting point of X_{2}Y_{2}and X_{3}Y_{3}as D.

**Observation**

Since AD is parallel to BC and DC is parallel to AB, ABCD is the required parallelogram

**Result**

ABCD is the required parallelogram having AB and BC as its two adjacent sides.

**Learning Outcome**

Without using protector and scale, we can construct a parallelogram by paper folding of any measurement.

**Activity Time**

Students may construct parallelogram of sides 4cm and 6cm with different angles.

**Viva Voce**

**Question 1.**

What are the main conditions of a quadrilateral to be a parallelogram ?

**Answer:**

Opposite pair of sides must be equal and parallel.

**Question 2.**

Do the diagonals of a parallelogram bisect each other ?

**Answer:**

Yes.

**Question 3.**

What is the type of a parallelogram if its all the four sides are equal ?

**Answer:**

Rhombus.

**Question 4.**

What is the type of a parallelogram if its one of the angles is 90° ?

**Answer:**

Rectangle.

**Question 5.**

If the diagonals of a parallelogram become equal, then what will be the name of the parallelogram ?

**Answer:**

Rectangle.

**Question 6.**

In which type of parallelogram, all the sides are equal and diagonals are also equal ?

**Answer:**

Square.

**Question 7.**

Is kite shape a parallelogram ?

**Answer:**

No.

**Question 8.**

Is a rectangle a parallelogram ?

**Answer:**

Yes.

**Question 9.**

Why a trapezium is not a parallelogram ?

**Answer:**

In a trapezium, only one pair of sides is parallel but in a parallelogram, two pairs of sides are parallel.

**Multiple Choice Questions**

**Question 1.**

In a parallelogram, if one of the angles is 36°, what is the measure of its adjacent angle ?

(i) 144°

(ii) 72°

(iii) 18°

(iv) none of these

**Question 2.**

In a parallelogram, if one of the angles is 90°, what are measures of other angles ?

(i) 30°, 60°, 90°

(ii) all are of 90°

(iii) 60°, 30°, 45°

(iv) none of these

**Question 3.**

If in a parallelogram, two adjacent sides become equal, then what will be the shape of the parallelogram?

(i) rhombus

(ii) square

(iii) rectangle

(iv) none of these

**Question 4.**

In a quadrilateral, if the length of one pair of opposite sides is 3 cm and length of the other pair of opposite sides is 4 cm, then quadrilateral becomes a:

(i) parallelogram

(ii) trapezium

(iii) rhombus

(iv) none of these

**Question 5.**

In a square of side 10 cm, the length of the diagonal will be:

(i) √100 cm

(ii) 10√2 cm

(iii) 10 cm

(iv) none of these

**Question 6.**

In a rhombus, diagonals bisect each other at an angle of:

(i) 45° and 135°

(ii) 60° and 120°

(iii) 90°

(iv) none of these

**Question 7.**

In a rectangle, if length is 14 cm and breadth is 10 cm, then length of the diagonal will be:

(i) 2√74 cm

(ii) √74 cm

(iii) √24 cm

(iv) none of these

**Question 8.**

In a square, if one of its diagonals is 13cm, then what will be the length of other diagonal?

(i) 169 cm

(ii) 26 cm

(iii) 13 cm

(iv) none of these

**Question 9.**

ABCD is a parallelogram such that AC is a diagonal. The relationship between ar (∆ABC) and ar (∆ACD) will be

(i) ar (∆ABC) = ar (∆ACD)

(ii) ar (∆ABC) ≠ ar (∆CD)

(iii) ar (∆ABC) = 2 ar (∆ACD)

(iv) none of these

**Question 10.**

In a parallelogram, if one of the angles is 108°, then what will be the measure of its opposite angle ?

(i) 80°

(ii) 54°

(iii) 108°

(iv) none of these

**Answers**

- (i)
- (ii)
- (i)
- (i)
- (ii)
- (iii)
- (i)
- (iii)
- (i)
- (iii)

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