Class 8 - Mathematics
Practical Geometry- Exercise 4.4
Top Block 1
Question: 1. Construct the following quadrilaterals:
(i) Quadrilateral DEAR
DE = 4 cm, EA = 5 cm, AR = 4.5 cm,
∠E = 60°, ∠A = 90°
(ii) Quadrilateral TRUE
TR = 3.5 cm, RU = 3 cm, UE = 4 cm,
∠R = 75°, ∠U = 120°
Answer :
(i) Given: DE = 4 cm, EA = 5 cm,
AR = 4.5 cm, ∠E = 60°, ∠A = 90°
To construct: A quadrilateral DEAR.
Steps of construction:
(a) Draw a line segment DE = 4 cm.
(b) At point E, construct an angle of 60°
(c) Taking radius 5 cm, draw an arc from point E which intersects at A.
(d) Construct ∠A = 90° draw an arc of radius 4.5 cm with centre A which intersect at R.
(e) Join RD.
It is the required quadrilateral DEAR.
(ii) Given: TR = 3.5 cm, RU = 3 cm,
UE = 4 cm, ∠R = 75°, ∠U = 120°
To construct: A quadrilateral TRUE
Steps of construction:
(b) At point E, construct an angle of 60°
(c) Taking radius 5 cm, draw an arc from point E which intersects at A.
(d) Construct ∠A = 90° draw an arc of radius 4.5 cm with centre A which intersect at R.
(e) Join RD.
It is the required quadrilateral DEAR.
(ii) Given: TR = 3.5 cm, RU = 3 cm,
UE = 4 cm, ∠R = 75°, ∠U = 120°
To construct: A quadrilateral TRUE
Steps of construction:
Mddle block 1
(a) Draw a line segment TR = 3.5 cm.
(b) Construct an angle 75° at ∠R and draw an arc of radius 3 cm with R as centre, which intersects at U.
(c) Construct an angle of 120° at U and produce the side UE.
(d) Draw an arc of radius 4 cm with U as centre.
(e) Join UE and TE.
It is the required quadrilateral TRUE.
(b) Construct an angle 75° at ∠R and draw an arc of radius 3 cm with R as centre, which intersects at U.
(c) Construct an angle of 120° at U and produce the side UE.
(d) Draw an arc of radius 4 cm with U as centre.
(e) Join UE and TE.
It is the required quadrilateral TRUE.