Page 198 - ICSE Math 8

(c) It is possible to construct a quadrilateral PQRS in which PQ = 3 cm, QR = 6 cm, –P = 100° and
–S = 60°.
(d) Construction of a quadrilateral GLAM in which GL = 6.3 cm, –G = 100°, –L = 145°, LA = 7.8 cm
and –A = 115° is possible.
(e) If in a quadrilateral EFGH, –E – –G is equal to 0 then the quadrilateral is a parallelogram.

PRACTICE TIME

1. Construct a quadrilateral JUMP in which JU = 4.5 cm, UM = 7 cm, MP = JP = 6 cm and JM = 9.5 cm.
2. Construct a quadrilateral JINX in which JI = 5 cm, IN = 5 cm, JX = 4 cm, –J = 130° and –X = 50°.
3. Construct a quadrilateral DENT in which DE = 5.5 cm, EN = 4 cm, –D = 80°, –E = 100° and –N = 90°.
4. Construct a parallelogram SINK in which SI = 6.5 cm, IN = 5.5 cm and –S = 60°.
5. Construct a square BOND in which diagonal BN = 8 cm.
6. Construct a rhombus STAR in which diagonals SA = 6 cm and TR = 8 cm.
7. Construct a trapezium SOME in which SO || ME, SO = 5.5 cm, OM = 4 cm, SE = 5.5 cm and –O = 60º.
8. Construct a parallelogram MARK in which MA = 5 cm, –A = 110º, –RMA = 35º.
9. Construct a rectangle DATE in which DA = 4 cm and the diagonal DT = 5 cm.
10. Construct a rectangle CARE in which diagonal AE = 5.6 cm and the diagonals CR and AE intersect at O
such that –AOR = 45º.
11. Suppose you are helping your friend to layout a rectangular dining space adjoining his house. How can
you use the properties of diagonals to locate the four corners of the dining space?

THINK SMART

1. How can you create three 2. Move two matchsticks
quadrilaterals by moving to obtain two rectangles.
exactly 2 sticks?

Maths Lab Activity

Objective: To check the conditions of the construction of a quadrilateral

Material required: Cardboard strip (5 in number), pins (to make hinges),
a pair of scissors
Step 1: Take four cardboard strips of suitable lengths.

Step 2: With the help of pins, hinge the strips at the ends to form a
quadrilateral, as shown in the figure.
Step 3: Try to change the shape of the quadrilateral by pressing at the opposite
vertices. Isn’t it easy! This shows that different quadrilaterals can
be made from the same measure of the 4 sides.
Step 4: Add another strip in the form of a diagonal as shown in the figure.
Try to change the shape of the quadrilateral. If you observe carefully, now
it is not possible to do so.
Result: This shows that construction of a unique quadrilateral needs at least
5 building blocks (or dimensions). For example, 4 sides and 1 diagonal, etc.

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