"Question 1 Construct the following quadrilaterals. (i) Quadrilateral LIFT LI = 4 cm IF = 3 cm TL = 2.5 cm LF = 4.5 cm IT = 4 cm (ii) Quadrilateral GOLD OL = 7.5 cm GL = 6 cm GD = 6 cm LD = 5 cm OD = 10 cm (iii) Rhombus BEND BN = 5.6 cm DE = 6.5 cm
Practical Geometry Page 62"
Answers
To construct a quadrilateral it is necessary to know at least 5 of its parts.
Measurement of 5 parts of a quadrilateral are sufficient to construct it in the following cases:
1. Four sides and one Diagonal.
2. Three sides and both diagonals.
3. Two adjacent sides and 3 angles.
4. Three sides and two included angles.
5. Four sides and one angle.
It is always convenient and helpful to draw a rough sketch of the quadrilateral and indicate the given measurements.
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[ Figure is in the attachment]
Steps of construction:
(a) Draw a line segment LI = 4 cm.
(b) Taking radius 4.5 cm, draw an arc taking L as centre.
(c) Draw an arc of 3 cm taking Las centre which intersects the first arc at F.
(d) Join FI and FL.
(e) Draw another arc of radius 2.5 cm taking L as centre and 4 cm taking I as centre which intersect at T.
(f) Join TF, Tl and TI.
It is the required quadrilateral LIFT.
ii)
(a) Draw a line segment OL = 7.5 cm
b) Draw an arc of radius 5 cm taking L as centre and another arc of radius 10 cm taking O as centre which intersect the first arc point at D.
(c) Join LD and OD.
(d) Draw an arc of radius 6 cm from D and draw another arc of radius 6 cm taking L as centre, which intersects at G.
(e) Join GD and GO.
It is the required quadrilateral GOLD.
(a) Draw segment DE = 6.5 cm.
(b) Draw perpendicular bisector of line segment DE.
(c) Draw two arcs of radius 2.8 cm from intersection point O, which intersects the line KN at B and N.
(d) Join BE, BD as well as ND and NE.
It is the required rhombus BEND.
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Hope this will help you....
