GSEB Class 8 Maths Solutions 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
GO = 7.5 cm
OL = 7.5 cm
GL = 6 cm
GD = 6 cm
LD = 5 cm
(iii) Rhombus BEND
BN = 5.6 cm
DE = 6.5 cm
Answer:
(i) Steps of construction for Quadrilateral LIFT:
I. First, draw a line segment LI that is 4 cm long.
II. Next, using I as the center and a radius of 4 cm, draw an arc.
III. Then, using L as the center and a radius of 2.5 cm, draw another arc. This arc will cross the first arc at point T.
IV. Join the points TI and TL to complete the first part.
V. With I as the center and a radius of 3 cm, draw another arc on the side opposite to L.
VI. With L as the center and a radius of 4.5 cm, draw a third arc to intersect the previous arc at point F.
VII. Finally, join FI and FL.
Thus, LIFT is the needed quadrilateral.

Exam Tip: When constructing a quadrilateral, always start by drawing one side as a base. Then, use compasses and arcs from the endpoints of that base to locate the other vertices, following the given side lengths and diagonals.

Answer:
(ii) Steps of construction for Quadrilateral GOLD:
I. Begin by drawing a line segment LD which is 5 cm long.
II. Using L as the center and a radius of 6 cm, draw an arc.
III. Now, with D as the center and a radius of 6 cm, draw another arc. This arc should cross the previous arc at point G.
IV. Join the points GL and GD to form a triangle.
V. Next, using D as the center and a radius of 10 cm, draw an arc on the side opposite to G.
VI. With L as the center and a radius of 7.5 cm, draw another arc that intersects the previous arc at point O.
VII. Finally, join OL and OD.
Thus, GOLD is the needed quadrilateral.

Exam Tip: For quadrilaterals where diagonals are given, it's often easiest to draw one diagonal first and use it as a base to construct the two triangles that make up the quadrilateral.

Answer:
(iii) Steps of construction for Rhombus BEND:
I. First, draw a line segment DE that is 6.5 cm long.
II. Next, draw the perpendicular bisector PQ of DE. Let M be the mid-point of DE.
III. Using M as the center and a radius of \( \frac { 1 }{ 2 } \times 5.6 \) cm \( = 2.8 \) cm, draw arcs to cross PQ at points B and N.
IV. Finally, join the points ND, NE, BE, and BD.
Thus, BEND is the needed rhombus.

Exam Tip: When constructing a rhombus using diagonals, remember that the diagonals bisect each other at right angles. This means you can draw one diagonal, find its midpoint, and then draw the perpendicular bisector to mark off half the length of the second diagonal on either side.