Page 197 - ICSE Math 8

5. Construct a parallelogram WING in which WI = 5 cm, IN = 4.5 cm and diagonal WN = 7.5 cm. Measure
the length of the other diagonal.
6. Construct a kite ROSE in which RO = 4.5 cm, OS = 5.4 cm and one of the diagonals RS = 7.7 cm.
[Hint: Kite is a quadrilateral with two pairs of adjacent sides equal.]
7. Construct a rhombus MARS with MA = 5 cm and MR = 7 cm. Measure the length of the other diagonal.
8. Construct a rhombus SURF in which diagonal SR = 4.8 cm and diagonal FU = 5.4 cm. Find the side of
the rhombus.
9. Construct a rhombus DIRT in which diagonal DR = 3.6 cm and diagonal TI = 4.5 cm.
10. Construct a trapezium WIND in which WI = 8.5 cm, IN = 5 cm, ND = 4.5 cm, –I = 60º and WI || ND.

AT A GLANCE

¾ To construct a quadrilateral uniquely, it is necessary to know at least five of its building blocks.
¾ To construct a quadrilateral, measurements of the following are sufficient:
(a) Four sides and one diagonal
(b) Three sides and two diagonals
(c) Two adjacent sides and three angles
(d) Three sides and two included angles
(e) Four sides and one angle
¾ The five building blocks, in order to be sufficient for construction of quadrilateral, must also satisfy
(wherever relevant):
(a) The triangle inequality property
(b) Angle-sum property of a quadrilateral
¾ It is also possible to construct special types of quadrilaterals (e.g., parallelogram, rectangle, etc.) with
less than five building blocks using some other relations between these blocks.
¾ If four angles and a side of a quadrilateral are given, then the quadrilateral cannot be constructed uniquely.

MENTAL MATHS

1. Choose the correct option.
(a) To construct a convex quadrilateral uniquely, it is necessary to know at least ____________ of its
building blocks.
(i) four (ii) five (iii) six (iv) three
(b) To construct a quadrilateral uniquely, we must know at least ____________ sides and two diagonals.
(i) one (ii) two (iii) three (iv) four
(c) A quadrilateral cannot be constructed uniquely, if its ____________ angles and ___________ side
are given.
(i) four, one (ii) three, one (iii) four, two (iv) none of these
(d) In a ____________ , both pairs of opposite sides are equal and all angles are of 90°.
(i) square (ii) rectangle (iii) rhombus (iv) parallelogram
(e) In a ____________ , all sides are equal and all angles are 90°.
(i) parallelogram (ii) rhombus (iii) square (iv) rectangle
2. Write True or False.
(a) A quadrilateral is a polygon with 4 sides, 4 enclosed angles and 2 diagonals.
(b) It is possible to construct a convex quadrilateral if the measure of its 3 angles and 2 diagonals are
given.

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