Question

"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) Parallelogram HEAR HE = 5 cm EA = 6 cm ∠R = 85° (iv) Rectangle OKAY OK = 7 cm KA = 5 cm

Practical Geometry Page 64"

Answer 1

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:

i)

(a) Draw a line segment MO = 6 cm.

(b) Construct ∠R =105°  and taking radius 4.5 cm, draw an arc taking O as centre, which intersects at R.

(c) Also construct an angle  105° at R and produce the side RE.

(d) Construct 

∠M=60°  and produce the side ME. Both sides ME and RE intersect at E.

It is the required quadrilateral MORE.

ii)

we have to find ∠L

= 360° -(90°+85°+110°)

= 360° –(285°)

∠L=75°

(a) Draw a line segment PL = 4 cm.

(b) Construct ∠P=90°  and produce the side PN.

(c) Construct ∠L=75°  and with L as centre, draw an arc of radius 6 cm, which intersects at A.

(d) Construct an  ∠A = 110°  and produce the side AN which intersects PN at N.

It is the required quadrilateral PLAN.

iii)

we have to find   ∠H

= 180° – 85°= 95°

∠H=95°

 Sum of adjacent angle of ||gm is 180°]

(a) Draw a line segment HE = 5 cm.

(b) Construct ∠H =  95° and draw an arc of radius 6 cm with centre H. It intersects AR at R.

(c) Join RH.

(d) Draw ∠R = ∠E = 85° and draw an arc of radius 6 cm with E as a centre which intersects RA at A.

(e) Join RA

It is the required parallelogram HEAR.

iv)

(a)  Draw a line segment OK = 7 cm.

(b) Construct ∠O=90 °and ∠K=90 ° and produce these sides.

(c) Draw two arcs of radius 5 cm from points O and K respectively. These arcs intersect at Y and A.

(d) Join YA.

It is the required rectangle OKAY.

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Hope this will help you....