This document contains solutions to 8 questions about constructing different geometric shapes given specific measurements of their sides or diagonals. The shapes constructed include quadrilaterals, parallelograms, rhombuses, and kites. For each question, clear step-by-step instructions are provided to draw the appropriate arcs and lines to form the desired shape based on the given measurements. It is determined in one question that the requested quadrilateral cannot be constructed because one measurement violates the triangle inequality.

1. Question 1.
Construct a quadrilateral ABCD in which AB = 4.4 cm, BC = 4 cm, CD = 6.4 cm, DA
= 3.8 cm and BD = 6.6 cm.
Solution:
Steps of construction :
(i) Draw a line segment AB = 4.4 cm.
(ii) With centre A and radius 3.8 cm and with centre B and radius 6.6 cm, draw arcs
intersecting each other at D.
(iii) With centre B and radius 4 cm, and with centre D and radius 6.4 cm, draw arcs
intersecting each other at C on the other side of BD.
(iv) Join AD, BD, BC and DC.
The ABCD is the required quadrilateral.
Question 2.
Construct a quadrilateral ABCD such that AB = BC = 5.5 cm, CD = 4 cm, DA = 6.3
cm and AC = 9.4 cm. Measure BD.
Solution:
(i) Draw a line segment AC = 9.4 cm.
(ii) With centre A and C and radius 5.5 cm, draw arcs intersecting each other at B.
(iii) Join AB and CB.
(iv) Again with centre A and radius 6.3 cm, and with centre C and radius 4 cm, draw
arcs intersecting each other at D below the line segment AC.
(v) Join AD and CD.
Then ABCD is the required quadrilateral. On measuring BD, it is 5 cm.
Question 3.
Construct a quadrilateral XYZW in which XY = 5 cm, YZ = 6 cm, ZW = 7 cm, WX = 3
cm and XZ = 9 cm.
Solution:
Steps of construction :
(i) Draw a line segment XZ = 9 cm.
(ii) With centre X and radius 3 cm and with centre Z and radius 7 cm, draw arcs
intersecting each other at W.

2. (iii) Join XW and ZW.
(iv) Again with centre X and radius 5 cm and with centre Z and radius 6 cm, draw
arcs, intersecting each other at Y below the line segment XZ.
(v) Join XY and ZY.
Then XYZW is the required quadrilateral.
Question 4.
Construct a parallelogram PQRS such that PQ = 5.2 cm, PR = 6.8 cm and QS = 8.2
cm.
Solution:
Steps of construction:
In a parallelogram, diagonals bisect each other. Now
(i) Draw a line segment PQ = 5.2 cm.
(ii) With centre P and radius 3.4 cm ((frac { 1 }{ 2 }) of PR) and with centre Q and
radius 4.1 cm ((frac { 1 }{ 2 }) of QS) draw arcs intersecting each other at O.
(iii) Join PQ and QO and produced them to R and S respectively such that PO = OR
and QO = OS.
(iv) Join PS, SR and RQ.
Then PQRS is the required parallelogram.
Question 5.
Construct a rhombus with side 6 cm and one diagonal 8 cm. Measure the other
diagonal.
Solution:
Steps of construction :
Sides of a rhombus are equal.
(i) Draw a line segment AC = 8 cm.

3. (ii) With centres A and C and radius 6 cm, draw two arcs above the line segment AC
and two below the line segment AC, intersecting each other at D and B respectively.
(iii) Join AB, AD, BC and CD.
Then ABCD is the required rhombus.
JoinBD.
On measuring BD, it is approximately 9 cm
Question 6.
Construct a kite ABCD in which AB = 4 cm, BC = 4.9 cm and AC = 7.2 cm.
Solution:
Steps of construction :
(i) Draw a line segment AC = 7.2 cm.
(ii) With centre A and radius 4 cm draw an arc.
(iii) With centre C and radius 4.9 cm, draw another arc which intersects the first arc
at B and D.
(iv) Join AB, BC, CD and DA.
Then ABCD is the required kite.
Question 7.
Construct, if possible, a quadrilateral ABCD given, AB = 6 cm BC = 3.7 cm, CD = 5.7
cm, AD = 5.5 cm and BD = 6.1 cm. Give reasons for not being able to construct, if
you cannot.
Solution:
Steps of construction :
(i) Draw a line segment BD = 6.1 cm.
(ii) With centre B and radius 6 cm and with centre D and radius 5.5 cm, draw arcs
intersecting at A.

4. (iii) Join AB and AD.
(iv) Again with centre B and radius 3.7 cm and with centre D and radius 5.7 cm, draw
two arcs intersecting each other at C below the BD.
(v) Join BC and DC.
Then ABCD is the required quadrilateral.
Question 8.
Construct, if possible a quadrilateral ABCD in which AB = 6 cm, BC = 7 cm, CD = 3
cm, AD = 5.5. cm and AC = 11 cm. Give reasons for not being able to construct, if
you cannot.
Solution:
Steps of construction:
It is not possible to construct this quadrilateral ABCD because
AD + DC = 5.5 cm + 3 cm = 8.5 cm
and AC = 11 cm
AD + DC < AC.
But we know that in a triangle,
Sum of two sides is always greater than its third side.