Page 194 - ICSE Math 8

3. Taking E as centre and radius = 5 cm, draw an arc on EX intersecting X
it at point A. A
4. At point A on line EA, make –EAY = 90º using a
protractor. 4.5 cm 90º
5. Taking A as centre and radius = 4.5 cm, draw an arc R 5 cm
on AY intersecting it at point R. Joint RD. Y
Hence, DEAR is the required quadrilateral.
60º
D 4 cm E

EXERCISE 17.4

1. Construct a quadrilateral FUSE in which FU = 5.2 cm, US = 4.6 cm, SE = 5.8 cm, ∠U = 30º and
∠S = 150º.
2. Construct a quadrilateral PINE in which PI = 3.5 cm, IN = 5.5 cm, NE = 5 cm, ∠I = 125º and ∠N = 80º.
3. Construct a quadrilateral PACE in which PA = 5.4 cm, AC = 5.7 cm, PE = 4.5 cm, ∠P = 120º and
∠A = 115º. What is the measure of the side CE?
4. Construct a quadrilateral MUST in which MU = 8 cm, US = 4 cm, ST = 6 cm, ∠U = 40º and ∠S = 85º.
5. Construct a quadrilateral DART in which AR = 5.6 cm, RT = 3.4 cm, DT = 4.6 cm, ∠R = 90º and
∠T = 105º.

Construction of a Quadrilateral Given 3 Angles and 2 Included Sides S
Example 5: Construct a quadrilateral MARS in which MA = 5.2 cm,
AR = 3.8 cm, –M = 100º, –A = 65º and –R = 130º. 130º R
Solution: Construction: Draw a rough sketch of the figure to be 3.8 cm
constructed. 100º 65º
5.2 cm
Steps of Construction: M Rough sketch A

1. Draw a line MA = 5.2 cm. X
2. At point M on line MA, draw –AMX = 100º. Also at point S Y
A on line MA, draw –MAY = 65º using a protractor. R

3. Taking A as centre and radius = 3.8 cm, draw an arc on
line AY intersecting it at point R. 130º

4. At point R on line AR, draw –ARS = 130º using a protractor 3.8 cm
intersecting line MX at S. Join RS.
100º 65º
Hence, MARS is the required quadrilateral. M 5.2 cm A

EXERCISE 17.5

1. Construct a quadrilateral MIKE in which MI = 5 cm, IK = 4 cm, ∠M = 80º, ∠I = 85° and ∠K = 125º.
2. Construct a quadrilateral WEST in which WE = 5 cm, ES = 3.2 cm, ∠W = 55º, ∠E = 100º and ∠T = 90º.
3. Construct a quadrilateral BUNK in which BU = 4 cm, UN = 7 cm, ∠B = 110º, ∠N = 110º and ∠K = 80º.
4. Construct a quadrilateral TURN in which UR = 4.7 cm, RN = 5.8 cm, ∠T = 60º, ∠U = 100º and
∠R = 70º.

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