## Chapter 4 Practical Geometry Exercise 4.3

Question 1: Construct the following quadrilaterals.

i) Quadrilateral MORE

MO = 6 cm

OR = 4.5 cm

∠M = 60°

∠O = 105°

∠R = 105°

ii) Quadrilateral PLAN

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N = 85°

iii) Quadrilateral HEAR

HE = 5 cm

EA = 6 cm

∠R = 85°

iv) Quadrilateral OKAY

OK = 7 cm

KA = 5 cm

Answer:

i)

Given

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N = 85°

Rough figure

Actual figure

Steps of Construction

1. Draw line segment MO = 6 cm.

2. Make ∠OMX = 60°.

3. Make ∠MOY = 105°.

4. With O as centre, radius 4.5 cm draw an arc to cut ray OY at R.

5. Make ∠ORZ = 105°.

6. Let ray MX and ray RZ intersect at E.

7. MORE is the required quadrilateral.

ii)

Given

Quadrilateral PLAN

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N = 85°

Rough figure

Angle sum property of quadrilateral = 360°

= 85° + 90° + 110° + x = 360°

= 285° + x = 360°

= x = 360° - 285°

= x = 75°

Actual figure

Steps of Construction

1. Draw line segment AL = 6.5 cm.

2. Make ∠LAZ = 110°

3. Make ∠ALX = 75°.

4. With L as centre, radius 4 cm draw an arc to cut ray XL at P.

5. Make ∠LPX = 90°.

6. Let ray AX and ray PY intersect at N.

7. PLAN is the required quadrilateral.

iii)

Given

Quadrilateral HEAR

HE = 5 cm

EA = 6 cm

∠R = 85°

Rough figure

∠E = 85° (Opposite angles are equal)

Angle sum property of quadrilateral = 360°

= 85° + x + 85° + x = 360°

= 170° + 2x = 360°

= 2x = 360° - 170°

= 2x = 190°

= x = 190/2

= x = 95°

Actual figure

Steps of Construction

1. Draw line segment AE = 6 cm.

2. Make ∠XAE = 95°.

3. Make ∠YEA = 85°.

4. With E as centre, radius 5 cm draw an arc to cut ray EY at H.

5. Make ∠EHZ = 95°.

6. Let ray AX and ray HZ intersect at R.

7. HEAR is the required quadrilateral.

iv)

Given

Quadrilateral OKAY

OK = 7 cm

KA = 5 cm

Rough figure

Actual figure

Steps of Construction

1. Draw line segment YA = 7 m.

2. Make ∠QYA = 90°.

3. Make ∠PAY = 90°.

4. With A as centre, radius 5 cm draw an arc to ray AP at K.

5. Make ∠AKR = 90°.

6. Let ray QY and ray KR intersect at O.

7. OKAY is the required quadrilateral.

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