NCERT Solutions Class 8th Maths Chapter – 4 Practical Geometry Exercise 4.1

1. Construct the following quadrilaterals.
(i) Quadrilateral ABCD AB = 4.5 cm
BC = 5.5 cm
CD = 4 cm AD = 6 cm AC = 7 cm

Solution:

The rough sketch of the quadrilateral ABCD can be drawn as follows.

(1) ∆ABC can be constructed by using the given measurements as follows.

(2) Vertex D is 6 cm away from vertex A. Therefore, while taking A as centre, draw an arc of radius 6 cm.

(3) Taking C as centre, draw an arc of radius 4 cm, cutting the previous arc at point D. Joint D to A and C.

ABCD is the required quadrilateral.

(ii) Quadrilateral JUMP JU = 3.5 cm
UM = 4 cm MP = 5 cm PJ = 4.5 cm PU = 6.5 cm
Solution:

The rough sketch of the quadrilateral JUMP can be drawn as follows.

(1) ∆ JUP can be constructed by using the given measurements as follows.

(2) Vertex M is 5 cm away from vertex P and 4 cm away from vertex U. Taking P and U as centres, draw arcs of radii 5 cm and 4 cm respectively. Let the point of intersection be M.

(3) Join M to P and U.

JUMP is the required quadrilateral.

(iii) Parallelogram MORE
OR = 6 cm

Solution:
RE = 4.5 cm
EO = 7.5
We know that opposite sides of a parallelogram are equal in length and also these are parallel to each other.
i.e., ME = OR, MO = ER

The rough sketch of the parallelogram MORE can be drawn as follows.

(1) ∆ EOR can be constructed by using the given measurements as follows.

(2) Vertex M is 4.5 cm away from vertex O and 6 cm away from vertex E. Therefore, while taking O and E as centres, draw arcs of 4.5 cm radius and 6 cm radius respectively. These will intersect each other at point M.

(3) Join M to O and E.

MORE is the required parallelogram.

(iv) Rhombus BEST
BE = 4.5 cm
ET = 6 cm

Solution: We know that all sides of a rhombus are of the same measure. Hence, BE = ES = ST = TB The rough sketch of the rhombus BEST can be drawn as follows.

(1) ∆ BET can be constructed by using the given measurements as follows.

(2) Vertex S is 4.5 cm away from vertex E and also from vertex T. Therefore, while taking E and T as centres, draw arcs of 4.5 cm radius, which will be intersecting each other at point S.

(3) Join S to E and T.

BEST is the required rhombus.