CONSTRUCTION OF QUADRILATERALS
I. Choose the correct option.
1.Find
the angle measures x in the following figure:
(A) 60o
2.The
(B) 50o
(C) 45o
(D) 90o
sum of the measures of the external angles of any polygon is
(A) 180o
3.Find
(B) 360o
(C) 270o
(D) 540o
x in the following figure:
(A) 110o
4.Which
(B) 108o
(C) 105o
(D) 100o
of the following statement is false in the following statements?
(A) The opposite sides of a parallelogram are of equal length.
(B) A kite has 4 sides.
(C) The opposite angles of a parallelogram are of equal measure.
(D) The adjacent angles in a parallelogram are complementary
5.Two
adjacent sides AB and BC of a parallelogram ABCD are in the ratio of 5:3. If the
perimeter is 200 cm, find the lengths of AB and BC.
(A) 25 cm, 50 cm
(B) 40 cm, 37.50 cm
(C) 62.50 cm, 37.50 cm
(D) 60 cm, 62.50 cm
6.The
measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the
measure of each of the angles of the parallelogram.
(A) 120o, 60o, 90o and 90o
(B) 110o, 70o, 90o and 90o
(C) 100o, 70o, 90o and 90o
(D) 108o, 108o, 72o and 72o
7.In
the given figure, ABCD is a parallelogram. Find the angle measures x, y and z.
(A) 110o, 20o and 30o
(B) 130o, 20o and 30o
(C) 120o, 20o and 40o
(D) 120o, 30o and 40o
8.Which
of the following statement is true?
(A) Opposite angles are supplementary in parallelogram.
(B) Diagonals bisect each other at right angle in rectangle.
(C) Diagonals are not equal in square.
(D) Diagonals bisect each other at right angle in rhombus.
9.Find
the number of sides of a regular polygon whose each exterior angle has a measure of
60o.
(A) 6
(B) 8
10.Find
(B) 60o
11.Two
(D) 5
the measure of each exterior angle of a regular polygon of 9 sides.
(A) 45o
(C) 40o
(D) 35o
adjacent sides of a parallelogram are 5 cm and 4 cm respectively. Find its perimeter.
(A) 18 cm
12.The
(C) 12
(B) 14 cm
(C) 10 cm
(D) 16 cm
diagonal of a rhombus are 6 cm and 8 cm, find the length of all sides of rhombus.
(A) 3 cm
(B) 6 cm
(C) 4 cm
(D) 5 cm
13.The
point of intersection of the diagonal of a quadrilateral divides one diagonal in the ratio
1:2. Can it be a parallelogram?
(A) No
(B) Yes
14.Diagonals
(C) May be
(D) None of them
of a square are equal and bisect each other at. ……
(A) 90o
(B) 60o
(C) 75o
(D) None of them
15.The
angle between the altitudes of a parallelogram, through the same vertex of an obtuse
angle of the parallelogram is 60 degree. Find the angles of the parallelogram.
(A) 150o, 120o, 60o and 30o
(B) 150o, 150o, 30o and 30o
(C) 120o, 60o, 90o and 45o
(D) None of them
16.How
(A) 9
many diagonals have a regular hexagon?
(B) 5
17.The
(C) 7
(D) 8
angles of a quadrilateral are in the ratio 3: 4: 5: 6. Find the measure of each angle.
(A) 60°, 90°, 100° and 110°
(B) 75°, 85°, 90° and 110°
(C) 60°, 80°, 100° and 120°
(D) 80°, 85°, 95° and 100°
18.In
the given figure, find the measure of the
BAD .
(A) 80°
(B) 70°
(C) 90°
(D) 105°
19.If
an angle of a parallelogram is two-third of its adjacent angle; find these two angles of the
parallelogram.
(A) 108o, 72o
(B) 110o, 70o
(C) 100o, 80o (D) 120o, 60o
the measure of all the angles of a || gm, if one angle is 24 o less than twice the smallest
angle.
20.Find
(A) 60o, 60o, 120o and 120o
(B) 45o, 45o, 120o and 120o
(C) 65o, 65o, 125o and 125o
(D) 68o, 68o, 112o and 112o
21.In
the given figure, ABCD is a parallelogram. Determine the measure of x.
(A) 135o
22.The
(B) 60o
(C) 120o
(D) 90o
sides BA and DC of a quadrilateral ABCD are produced as shown in the given figure.
Find the sum of angle EAD and angle BCF.
(A) 200o
23.State
24.Find
(B) 180o
(C) 150o
(D) 210o
the name of a regular polygon of 8 sides
the angle measure of x in fig 1.
Fig. 1
II. Solve the following.(2M)
25.Draw a quadrilateral PQRS where PQ= QR= 5cm, RS= 7cm, SP= 6cm and
26.Construct a rhombus
R = 80˚
with side 5.5cm and one of the angles 70˚
27.Draw a quadrilateral MNOP where MN = 3cm, NO = 5cm, OP = 5cm, PM = 4cm and
N = 100˚
28.Draw a Rhombus with a diagonal 8.5cm and one side 6.3cm.
29.Draw a rectangle with two
adjacent sides 10cm and 8cm
30.Draw a square with side 5cm
III. Solve the following.(3M)
31.Is it possible to construct a quadrilateral ABCD
if
a) AB = BC = CD = DA = 5cm
b) AB = 10cm, BC = 8.5cm, CD = 15cm, DA = 12cm, CA = 11cm and BD = 18cm.
32.Construct
Quadrilaterals UV= 5.5cm VW=6cm, U=140o, V=90o and X=130o.
33.Construct
Quadrilateral UV=VW=5cm, U=100o, V=120o,and W=40o.
34.Construct
Quadrilateral U=V=80o, X=150o, W=50o and UV=6cm.
35.Construct
36.Construct
O=125 .
a Square in which the diagonal is of length 4cm.
Trapezium MNOP in which MN||PO, M=55o, MN=2.8cm, PM=4.2cm and
o
37.A
Parallelogram in which two adjacent sides are of length 5.5cm and 4cm and diagonal is
of length 6.5cm.
38.Construct
39.A
rhombus in which a diagonal are of length 8.5cm and 6.2cm.
rhombus with a side 6.5cm and one of the angle 50o.
IV. Solve the following.(4M)
40.Two
adjacent angles of a parallelogram have equal measure. Find the measures of each of
the angles of the parallelogram.
41.Name
the Quadrilaterals whose diagonals
(i) Bisect each other
(ii) Are perpendicular bisector of each other
42.Two
adjacent angles of a Parallelogram are (3x -4) and (3x + 10). Find the angles of the
Parallelograms.
V. Solve the following.(5M)
43.Construct a quadrilateral PQRS
in which PQ = 4.5cm, QR = 4cm, RS = 5cm, PR = 6.5cm, QS = 7.5cm
44.Construct a quadrilateral UVWX
in which UV = 3.2cm, VW = 4.8CM, U =50˚, V =120˚, X = 100˚
45.Construct
46.Construct
a rectangle in which two adjacent sides are 3cm and 4cm.
Quadrilateral ABCD where AB=5cm, BD=6cm, CD=5.8cm, DA=4.3cm, BC=5.5cm.
47.Construct
Quadrilateral MNOP where MN=3cm, NO=5cm, OP=5cm, PM=4cm and N=100o.
48.Rhombus
with a diagonal 8.5cm and one side 6.3cm.
49.Construct
Quadrilateral IJKL in which IJ=4cm, JK=2.9cm, KL=3.6cm, LI=4.2cm, JL=5.2cm.
50.Construct
Parallelogram QRST in which QR=6cm, RS=4cm, and S=45o.
51.Rhombus
a side 4cm and one angle 75o.