## CBSE Class 9 Maths Lab Manual – Parallelogram

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

Prerequisite Knowledge

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

Materials Required
Glazed papers, pen, pencil, scale.

Procedure

1. 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.
2. 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 X1Y1 ⊥BC and unfold the paper.
3. 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 X2Y2.
4. Fold the paper along the line that passes through the point C which is parallel to the line AB and cuts the line X2Y2. Make a crease and unfold it. Draw the line X3Y3 parallel to AB. Mark the intersecting point of X2Y2 and X3Y3 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 ?
Opposite pair of sides must be equal and parallel.

Question 2.
Do the diagonals of a parallelogram bisect each other ?
Yes.

Question 3.
What is the type of a parallelogram if its all the four sides are equal ?
Rhombus.

Question 4.
What is the type of a parallelogram if its one of the angles is 90° ?
Rectangle.

Question 5.
If the diagonals of a parallelogram become equal, then what will be the name of the parallelogram ?
Rectangle.

Question 6.
In which type of parallelogram, all the sides are equal and diagonals are also equal ?
Square.

Question 7.
Is kite shape a parallelogram ?
No.

Question 8.
Is a rectangle a parallelogram ?
Yes.

Question 9.
Why a trapezium is not a parallelogram ?
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

1. (i)
2. (ii)
3. (i)
4. (i)
5. (ii)
6. (iii)
7. (i)
8. (iii)
9. (i)
10. (iii)