## Chapter 4 Practical Geometry Exercise 4.2

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

Answer:

i)

Given

Quadrilateral LIFT

LI = 4 cm

IF = 3 cm

TL = 2.5 cm

LF = 4.5 cm

IT = 4 cm

Rough figure

Actual figure

Steps of Construction

1. Draw line segment LF = 4.5 cm.

2. With L as centre, radius 4 cm draw an arc.

3. With F as radius, radius 3 cm draw an arc to cut previous arc at I.

4. With L as centre, radius 2.5 cm draw an arc.

5. With I as centre, radius 4 cm draw an arc to cut previous arc at T.

6. Join LT, LI, TF, FT.

7. LIFT is the required quadrilateral.

ii)

Given

Quadrilateral GOLD

OL = 7.5 cm

GL = 6 cm

GD = 6 cm

LD = 5 cm

OD = 10 cm

Rough figure

Actual figure

Steps of Construction

1. Draw line segment OD = 10 cm.

2. With O as centre, radius 7.5 cm draw an arc.

3. With D as centre, radius 5 cm draw an arc to cut previous arc at L.

4. With D as centre, radius 6 cm draw an arc.

5. With L as centre, radius 6 cm draw an arc to cut the previous arc at G.

6. Join OL, DL, OG, DG.

7. GOLD is the required quadrilateral.

iii)

Given

Rhombus BEND

BN = 5.6 cm

DE = 6.5 cm

Rough figure

Actual figure

Steps of Construction

1. Draw line segment DE = 6.5 cm.

2. Draw the perpendicular bisector of DE to intersect DE at O (O is the midpoint of DE).

3. With O as the centre and radius = 2.8 cm, draw arcs on either sides to intersect the perpendicular bisector at B and N.

4. Join BD, BE, DN, EN.

5. BEND is the required rhombus.

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