# Practical Geometry Questions

We provide practical geometry practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on practical geometry skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom. #### List of practical geometry Questions

Question NoQuestionsClass
1Construct quadrilaterals to the given measurements; the order of the letters
in each case is ( A, B, C, D )
( A B=4.8 mathrm{cm}, B C=4.4 mathrm{cm}, C D=7 mathrm{cm}, D A= )
( 3.4 mathrm{cm}, mathrm{BD}=6.2 mathrm{cm} )
8
2Construct a quadrilateral ( boldsymbol{A B C D} ), with ( boldsymbol{B C}=mathbf{5} mathrm{cm}, boldsymbol{C D}=mathbf{9} mathrm{cm}, boldsymbol{D} boldsymbol{A}=mathbf{6} mathrm{cm} )
( angle C=60^{circ}, angle D=75^{circ} )
8
3Construct a quadrilateral ( A B C D ) with ( A B=9 c m, B C=6 c m, C D=7 c m )
( A C=9 c m ) and ( B D=11 mathrm{cm} )
8
4Arrange the following steps in correct order in constructing a square whose one diagonal is ( 5 mathrm{cm} ) Step 1: Let PQ cut AC at 0.
Step 2: Draw a diagonal ( A C=5 c m ) Step 3: Join ( A b, B C, C D ) and DA. Then ABCD is the required square. Step 4: Draw PQ the perpendicular bisector of AC.
Step 5: With 0 as centre and OA radius draw a circle. Let the circle cut QP at
points B and D.
A. 2,1,4,5,3
В. 2,5,4,1,3
c. 2,4,5,1,3
D. 2,4,1,5,3
8
5Construct ( triangle X Y Z ) in which ( X Y= )
( 4.5 mathrm{cm}, Y Z=5 mathrm{cm} ) and ( Z X=6 mathrm{cm} )
7
6Construct a quadrilateral ABCD, if ( A B=4.5 mathrm{cm}, mathrm{BC}=5.5 mathrm{cm}, mathrm{CD}=5 mathrm{cm}, mathrm{DA}=4.8 )
( mathrm{cm}, ) and ( angle A B C=60^{circ} )
8
7Construct a right angled triangle whose
hypotenuse measure ( 6.5 mathrm{cm} ) and one of
its acute angle measure ( 60^{circ} )
7
8Construct a ( triangle A B C, ) when ( A B= )
( A C, B C=6.0 mathrm{cm} ) and ( angle B=45^{circ} )
7
9Construct a quadrilateral ( boldsymbol{A B N V} ) where ( boldsymbol{A} boldsymbol{V}=mathbf{7} boldsymbol{c m}, boldsymbol{B} boldsymbol{A}=mathbf{8} boldsymbol{c m}, boldsymbol{B} boldsymbol{N}= )
( mathbf{1 0} c boldsymbol{m}, boldsymbol{N} boldsymbol{V}=mathbf{5} boldsymbol{c m} ) and ( boldsymbol{B} boldsymbol{V}=mathbf{1 1} boldsymbol{c m} )
The relation between diag. ( A N ) and
diag. ( boldsymbol{B} boldsymbol{V} ) is
A. ( A N>B V )
B. ( A N<B V )
c. ( A N=B V )
D. None of the above
8
10Construct the quadrilaterals with the given measurements.And write steps of construction.
quadrilateral ABCD with ( A B=5.5 c m )
( B C=3.5 c m, C D=4 c m, A D=5 c m )
and ( angle A=45^{circ} )
8
114.
Construct a rectangle PQRS with PQ = 5.5 cm and
OR=3 cm.
sastanal DODS with PO=6mand diagonal
8
124.
A quadrilateral can be drawn when all the four angles and
one side is given.
8
13of
1.
To construct a quadrilateral ABCD, which of the following
parts is necessary?
(a) Length of AB
(b) Length of BC
© Measure of ZA, ZB and ZC
(d) Both (a) and (b)
8
146. A parallelogram can be constructed uniquely if both
diagonals and the angle between them is given.
8
158.
Is it possible to construct a quadrilateral ABCD in which
AB=3 cm, BC=4 cm, CD=5.4 cm, DA=5.9 and diagonal
AC = 8 cm? If not, why?
8
given measures.
In Quadrilateral MORE: ( ell(M O)= )
( mathbf{5 . 8} boldsymbol{c m}, ell(boldsymbol{O} boldsymbol{R})=mathbf{4 . 4} boldsymbol{c m}, boldsymbol{m} angle boldsymbol{M}= )
( mathbf{5 8}^{circ}, boldsymbol{m} angle boldsymbol{O}=mathbf{1 0 5}^{circ}, boldsymbol{m} angle boldsymbol{R}=mathbf{9 0}^{circ} mathbf{?} )
8
17Arrange the given steps in CORRECT order, while constructing ( triangle P Q R ) where ( P M perp Q S ) and it is given that ( Q R=4.2 )
( mathrm{cm}, angle mathrm{Q}=120^{circ} ) and ( mathrm{PQ}=3.5 mathrm{cm} )
Step 1: Now, extend RQ to S and with P
as centre and with a sufficient radius,
draw an arc, cuffing ( mathrm{SQ} ) at ( mathrm{A} ) and ( mathrm{B} ). Step 2. Along QX, set off QP = 3.5 cm. Step 3. Draw a line segment ( Q R=4.2 mathrm{cm} )
and construct ( angle mathrm{RQX}=120^{circ} )
Step 4. Joint PR.
Step 5. Joint PC, meeting RQ product at
M. Then, PM ( perp ) QS
Step 6. With A as centre and radius
more than half ( A B, ) draw an arc. Now
with ( mathrm{B} ) as centre and with the same
radius draw another arc, cutting the previous arc at ( mathbf{C} )
A ( cdot 1 rightarrow 2 rightarrow 3 rightarrow 4 rightarrow 5 rightarrow 6 )
B . ( 4 rightarrow 1 rightarrow 2 rightarrow 3 rightarrow 5 rightarrow 6 )
( c cdot 2 rightarrow 4 rightarrow 3 rightarrow 1 rightarrow 5 rightarrow 6 )
D. ( 3 rightarrow 2 rightarrow 4 rightarrow 1 rightarrow 6 rightarrow 5 )
7
184.
Construct a quadrilateral ABCD, where AB=4 cm, BC =5
cm, CD=6.5 cm and ZB= 105º and ZC=80°.
Lai cibi te ontruthumbug ADCD where
8
19Construct a triangle ( A B C, ) whose base
( B C=6 c m, angle B=60^{circ} ) and altitude
( A D=4 mathrm{cm} )
7
20Construct ( Delta A B C ) in which ( A B=5 mathrm{cm} )
( angle B=45^{circ} ) and ( B C=6 c m )
7
21The angle of quadrilateral are ( boldsymbol{x}, boldsymbol{x}+ )
( 60,4 x, 2 x+30 ) find ( x )
8
22Construct a quadrilateral ( P Q R S ) in which ( boldsymbol{P Q}=mathbf{5} boldsymbol{c m}, boldsymbol{Q} boldsymbol{R}=mathbf{7 . 5 c m}, boldsymbol{R S}= )
( P S=6.5 c m, ) and ( P R=10 c m )
Measure the diagonal ( Q S )
8
23Construct a quadrilateral ( boldsymbol{V} boldsymbol{A} boldsymbol{B} boldsymbol{N} )
where ( boldsymbol{V} boldsymbol{A}=mathbf{7} boldsymbol{c m}, boldsymbol{A B}=boldsymbol{8} boldsymbol{c m}, boldsymbol{B} boldsymbol{N}= )
( mathbf{1 0} c boldsymbol{m}, boldsymbol{A} boldsymbol{N}=mathbf{1 2} boldsymbol{c m} ) and ( boldsymbol{V} boldsymbol{B}=mathbf{1 1} boldsymbol{c m} )
The measure of side ( V N ) is :
A. ( 6 mathrm{cm} )
B. ( 6.5 mathrm{cm} )
( c cdot 5 mathrm{cm} )
D. ( 5.2 mathrm{cm} )
8
24Construct a triangle ( A B C ), in which
( A B=5.5 c m, A C=6.5 c m ) and
( angle B A C=70^{circ} )
Steps for its construction is given in a jumbled form.Identify its correct
sequence
1) At ( A, ) construct a line segment ( A E )
sufficiently large, such that ( angle B A C ) at
( 70^{circ}, ) use protractor to measure ( 70^{circ} )
2) Draw a line segment which is sufficiently long using ruler.
3) With ( A ) as centre and radius ( 6.5 mathrm{cm} )
draw the line cutting ( A E ) at ( C ), join ( B C ),
then ( A B C ) is the required triangle.
4) Locate points ( A ) and ( B ) on it such that
( A B=5.5 c m )
A. 2,4,1,3
B. 2,1,4,3
c. 1,2,4,3
D. 4,2,1,3
7
25Construct ( triangle P Q R ) such that ( P Q=5 )
( mathrm{cm}, Q R=3 mathrm{cm} ) and ( angle Q=95^{circ} )
7
265. A quadrilateral can be drawn if three sides and two
diagonals are given.
8
272.
Construct a quadrilateral ABCD in which AB = 4.5 cm,
BC = 3 cm, CD = 3.2 cm, AD=2.5 cm and the diagonal
AC=5 cm.
8
28ng
Given AB=3 cm, BC = 5 cm, AC=9 cm, AD=6 cm, CD=2
cm. Which of the following is true about the construction
(a) It is possible to draw the quadrilateral.
DC<AC.
<AC
(d) None of these
8
298. Construct a rectangle PQRS given that PQ = 5 cm and the diagonal PR=6.5 cm.
. f
11.
l
otal
1
DOD
8
30Draw a triangle ( A B C ) with side ( B C= )
( mathbf{7} c boldsymbol{m}, angle boldsymbol{B}=mathbf{4 5}^{o}, angle boldsymbol{A}=mathbf{1 0 5}^{circ} . ) Then
construct a triangle whose side are ( frac{4}{3} )
times the corresponding sides of ( triangle A B C . ) Write the construction.
7
313.
be sufficient must also satisfy
inequality
of a triangle, wherever applicable.
and
8
32A quadrilateral can be drawn if only measures of four sides
are given.
8
33Construct a triangle ( X Y Z ) in which
( X Y=5 c m, Y Z=5.5 c m ) and
( angle X Y Z=100^{circ} )
7
34Construct a quadrilateral ( P Q R S ) with
( boldsymbol{P Q}=mathbf{8} mathrm{cm}, boldsymbol{Q} boldsymbol{R}=boldsymbol{6} mathrm{cm}, angle boldsymbol{P}= )
( mathbf{6 0}^{circ}, angle boldsymbol{Q}=mathbf{4 5}^{circ}, angle boldsymbol{R}=mathbf{6 0}^{circ} )
8
353.
MATHEMATICS
Construct a parallelogram ABCD, where AB =4.5 cm,
BC=3 cm and ZB = 1050
8
36Construct a ( triangle A B C ) with ( A B= )
( mathbf{3} c m, B C=4 c m ) and ( A C=5 c m ) and
find ( boldsymbol{m} angle boldsymbol{A} boldsymbol{C} boldsymbol{B}=boldsymbol{?} )
A .37
B. 53
( c cdot 60^{circ} )
D. ( 90^{circ} )
7
37Construct a quadrilateral ABCD with ( A B=2.5 mathrm{cm}, B C=3.5 mathrm{cm}, A D=4.5 mathrm{cm} )
( angle A=90^{0} ) and ( angle B=120^{0} )
8
383. Construct a quadrilateral ABCD given AB=5.6 cm, BC = 4.1 cm, CD=4.4 cm, AD=3.3 cm and ZA=75º.
Sol. Steps of Construction:
Draw AR=56cm
8
39-SULVED EXAMPLLJ
1. Construct a quadrilateral ABCD in which AB= 4.4 cm, BC = 4 cm, CD = 0.1
NAB= 4.4 cm, BC=4 cm, CD = 6.4 cm. DA=2.8 cm and BD= 6.6 cm
Sol. Steps of Construction :
8
402.
Construct a square LMNO whose diagonal is 6 cm.
Thea
: 1
:
1
:
1
Р
8
41The number of triangles with any three of the length 1,4,6 and ( 8 mathrm{cms}, ) as sides is
( A cdot 4 )
B. 2
( c cdot 1 )
D.
7
42Construct a quadrilateral ( A B C D ) in
which ( A B=B C=3.0 c m, A D= )
( C D=5.0 mathrm{cm} ) and ( angle A B C=120^{circ} )
8
43Construct a quadrilateral ( boldsymbol{A B N V} ) where ( boldsymbol{A} boldsymbol{V}=mathbf{7} boldsymbol{c m}, boldsymbol{B} boldsymbol{A}=mathbf{8} boldsymbol{c m}, boldsymbol{B} boldsymbol{N}= )
( mathbf{1 0} c boldsymbol{m}, boldsymbol{N} boldsymbol{V}=mathbf{5} boldsymbol{c m} ) and ( boldsymbol{B} boldsymbol{V}=mathbf{1 1} boldsymbol{c m} )
Then, the perimeter of ( Delta B N V ) is
( mathbf{A} cdot 26 mathrm{cm} )
B. ( 24 mathrm{cm} )
c. ( 28 mathrm{cm} )
D. ( 22 mathrm{cm} )
8
44Construct a triangle ( boldsymbol{A B C} ), where ( A B=4 c m, B C=5 c m ) and ( angle A B C= )
( 45^{circ} . ) Also, find the maximum length of
side ( boldsymbol{A C} )
7
( J U=3.5 mathrm{cm} )
( mathrm{UM}=4 mathrm{cm} )
( mathrm{MP}=5 mathrm{cm} )
( P J=4.5 mathrm{cm} )
( P U=6.5 mathrm{cm} )
8
46Complete the following, so as to make a
true statement:

The measures of each angle of a convex
quadrilateral is ( mathbf{1 8 0}^{circ} )

8
47What is the side included between the
angles ( mathrm{M} ) and ( mathrm{N} ) of ( triangle M N P ? )
7
48Construct ( Delta A B C ) in which ( A B=4.5 mathrm{cm} )
( A C=4.5 mathrm{cm} ) and ( angle B=50^{circ} . ) Check
whether you get two triangles.
7
with ( mathrm{EF}=5.2 mathrm{cm}, angle mathrm{GEF}=50^{circ}, mathrm{FG}=6 mathrm{cm} )
and ( angle mathrm{EGH}=40^{circ} )
8
50Construct a cyclic quadrilateral ( boldsymbol{P} boldsymbol{Q} boldsymbol{R} boldsymbol{S} )
in which ( boldsymbol{P Q}=mathbf{5} mathrm{cm}, boldsymbol{Q} boldsymbol{R}=boldsymbol{6} mathrm{cm}, boldsymbol{P} boldsymbol{R} )
( =3.5 mathrm{cm} ) and ( R S=5 mathrm{cm} )
8
51Construct a quadrilateral ( P Q R S ) in
which ( P Q=4.5 c m, Q R=5.2 mathrm{cm} )
( R S=5.5 c m, P S=4 c m ) and
( angle P Q R=120^{circ} )
8
52In the adjacent figure, the bisector of
( angle A ) and ( angle B ) meet in a point ( P . ) If ( angle C= )
( 100^{circ} ) and ( angle D=60^{circ}, ) find the measure
of ( angle A P B ).
8
53J.
11 quauillatai Laul lavuan ruui ansi
vuruc.
4.
A quadrilateral can be drawn when all the four angles and
one side is given.
8
54Draw a triangle ABC. Draw it’s median AD7
55To construct a parallelogram, the minimum number of measurements
required is
A. 5
B. 4
( c cdot 3 )
D.
8
56Construct a quadrilateral ( L I F T, ) when:
( boldsymbol{L} boldsymbol{I}=boldsymbol{4} boldsymbol{c m}, boldsymbol{I} boldsymbol{F}=boldsymbol{3} boldsymbol{c m}, boldsymbol{T} boldsymbol{L}= )
( 2.5 mathrm{cm}, L F=4.5 mathrm{cm}, I T=4 mathrm{cm} )
8
57The sides ( A B, B C, C A ) of a triangle ( A B C ) have 3,4 and 5 interior points
respectively on them. The number of triangles that can be constructed using these points as vertices is
A . 205
в. 210
c. 315
D. 216
7
58тре
( M O=6 mathrm{cm} )
( boldsymbol{O} boldsymbol{R}=mathbf{4 . 5} boldsymbol{c m} )
( angle M=60^{circ} )
( angle O=105^{circ} )
( angle R=105^{circ} )
(ii) Quadrilateral ( boldsymbol{P} boldsymbol{L} boldsymbol{A} boldsymbol{N} )
( boldsymbol{P L}=boldsymbol{4} boldsymbol{c m} )
( boldsymbol{L} boldsymbol{A}=mathbf{6 . 5} boldsymbol{c m} )
( angle boldsymbol{P}=mathbf{9 0}^{circ} )
( angle A=110^{circ} )
( angle N=85^{circ} )
(iii) Parallelogram ( boldsymbol{H} boldsymbol{E} boldsymbol{A} boldsymbol{R} )
( boldsymbol{H} boldsymbol{E}=mathbf{5} boldsymbol{c m} )
( boldsymbol{E} boldsymbol{A}=boldsymbol{6} boldsymbol{c m} )
( angle boldsymbol{R}=mathbf{8} mathbf{5}^{circ} )
(iv) Rectangle ( boldsymbol{O} boldsymbol{K} boldsymbol{A} boldsymbol{Y} )
( boldsymbol{O} boldsymbol{K}=mathbf{7} boldsymbol{c m} )
( boldsymbol{K} boldsymbol{A}=mathbf{5} boldsymbol{c m} )
8
59Construct a triangle ( A B C ) in which ( B C= )
( 8 c m, angle B=45^{0} ) and ( A B-A C=3.5 mathrm{cm} )
7
60Construct a quadrilateral ( A B C D, ) when
( A B=6.3 mathrm{cm}, B C=C D=4.2 mathrm{cm} ) and
( angle A B C=angle B C D=90^{circ} )
Find the length of side ( A D ) and
( boldsymbol{m} angle boldsymbol{B} boldsymbol{A} boldsymbol{D} )
A. ( A D=3.5 mathrm{cm}, 70^{circ} )
B. ( A D=4.7 mathrm{cm}, 65 )
C . ( A D=4.5 mathrm{cm}, 70^{circ} )
D. ( A D=3.5 mathrm{cm}, 65 )
8
61Construct a quadrilateral ( boldsymbol{V} boldsymbol{A} boldsymbol{B} boldsymbol{N} )
where ( boldsymbol{V} boldsymbol{A}=mathbf{7} boldsymbol{c m}, boldsymbol{A B}=boldsymbol{8} boldsymbol{c m}, boldsymbol{B} boldsymbol{N}= )
( mathbf{1 0} c boldsymbol{m}, boldsymbol{A} boldsymbol{N}=mathbf{1 2} boldsymbol{c m} ) and ( boldsymbol{V} boldsymbol{B}=mathbf{1 1} boldsymbol{c m} )
The perimeter (in cm.) of ( square V A B N ) is
8
62Are the triangle shown in Fig
congruent?why?
7
63Use ruler and compass only for the following question. All construction lines and arcs must be clearly shown. Construct a ( triangle A B C ) in which ( B C= )
( 6.5 c m, angle A B C=60^{circ}, A B=5 mathrm{cm} )
Construct a locus of points ( l_{1} ) at a
distance of ( 3.5 mathrm{cm} ) from ( A . ) Also,
construct a locus of points ( l_{2} ) which is
equidistant from ( A C ) and ( B C . ) Let ( l_{1} )
intersect ( l_{2} ) in two points ( X ) and ( Y )
Measure ( boldsymbol{X} boldsymbol{Y} )
7
64Construct a quadrilateral ( M O R E )
where ( M O=6 c m, O R= )
( 4.5 mathrm{cm}, angle M=60^{circ}, angle O=105^{circ} ) and
( angle R=105^{circ} )
8
65Construct a quadrilateral ( P Q R S ) with
( Q R=8 mathrm{cm}, R S=4 mathrm{cm}, S P=9 mathrm{cm} )
( boldsymbol{P Q}=mathbf{5 . 5} mathrm{cm} ) and ( boldsymbol{Q} boldsymbol{S}=boldsymbol{6} mathrm{cm} )
8
66Construct a quadrilateral ( A B C D, ) when
Angle ( boldsymbol{A}=mathbf{9 0}^{circ} boldsymbol{A B}=mathbf{4 . 6} mathrm{cm}, boldsymbol{B D}=mathbf{6 . 4} )
( mathrm{cm}, A C=6 mathrm{cm} ) and ( C D=4.2 mathrm{cm} )
8
67Draw a triangle with sides ( 5 mathrm{cm}, 6 mathrm{cm} ) and ( 6 mathrm{cm} . ) Draw a square having the same area as the triangle.7
68Complete the following, so as to make a
true statement:
A quadrilateral has vertices, no three of which are
8
69Construct a quadrilateral ( P Q R S ) in
which ( P Q=3.8 mathrm{cm}, Q R=3.4 mathrm{cm} )
( boldsymbol{R} boldsymbol{S}=mathbf{4 . 5} mathrm{cm}, boldsymbol{S} boldsymbol{P}=mathbf{5} mathrm{cm} ) and ( angle boldsymbol{Q}= )
( 80^{circ} . ) State which of these is the last
step.
A. From ( Q ), set ( Q R=3.4 mathrm{cm} )
B. With ( P ) as center and radius equal to ( 5 mathrm{cm} ), draw an arc
c. Join ( P S ) and ( R S )
D. Make ( angle P Q X=80^{circ} )
8
70Construct a ( triangle A B C, ) when ( A B= )
( 6.2 mathrm{cm}, A C=5.2 mathrm{cm} ) and ( angle B=45^{circ} )
7
71Construct a ( triangle boldsymbol{A B C}, boldsymbol{A B}= )
( mathbf{6 c m}, boldsymbol{B C}=mathbf{7} mathbf{c m} ) and ( angle boldsymbol{A}=mathbf{6 0}^{circ} )
7
72Draw a triangle ( P Q R ) in which ( P Q= )
( mathbf{7} boldsymbol{c m}, boldsymbol{Q} boldsymbol{R}=mathbf{3} boldsymbol{c m}, boldsymbol{R} boldsymbol{P}=mathbf{4} boldsymbol{c m} . ) Is the
construction of triangle possible?
7
73Construct, if possible, a quadrilateral ABCD given
AB=6 cm, BC = 3.7 cm, CD=5.7 cm, AD=5.5 and BD-
6.1 cm. Give reason for not being able to construct it,
if you cannot
8
74In a quadrilateral define the following:
Opposite angles
8
75ulagullas allu uu augiu Louw
****
A rhombus can be constructed uniquely if both diagonals
are given.
8
76Construct ( square ) DEFG such that ( l(mathrm{DE})=4.5 )
( mathrm{cm}, l(mathrm{EF})=6.5 mathrm{cm}, l(mathrm{DG})=5.5 mathrm{cm}, l(mathrm{DF}) )
( =mathbf{7} . mathbf{2} mathrm{cm}, l(mathrm{EG})=mathbf{7 . 8} mathrm{cm} )
8
77Construct a quadrilateral ABCD in which AB = 3.8 cm,
BC=5 cm, CD=5 cm, DA=5.5 cm and AC= 8 cm.
8
78Construct a ( triangle X Y Z ) such that:
( boldsymbol{Y} boldsymbol{Z}=mathbf{5} boldsymbol{c m}, angle boldsymbol{Z} boldsymbol{Y} boldsymbol{X}=mathbf{3 0}^{boldsymbol{o}} ) and
( angle Y Z X=75^{circ} )
7
79Construct ( triangle A B C ) such that ( A B= )
( 2.5 c m, B C=6 c m ) and ( A C=6.5 c m )
Measure ( angle B )
7
80Construct a quadrilateral ABCD with AB ( =4 mathrm{cm}, mathrm{BC}=6 mathrm{cm}, mathrm{CD}=5.6 mathrm{cm} mathrm{DA}=5 mathrm{cm} )
and ( A C=8 mathrm{cm} . ) Find also its area.
8
81Construct a ( triangle P Q R ) in which ( Q R= )
( mathbf{6} c boldsymbol{m}, boldsymbol{P Q}=mathbf{4 . 4} boldsymbol{c m} ) and ( boldsymbol{P} boldsymbol{R}=mathbf{5 . 3} boldsymbol{c m} )
Draw the bisector of ( angle P )
7
82Construct a triangle ( P Q R ) in which ( Q R=6 c m, angle Q=60^{circ} ) and ( P R- )
( boldsymbol{P Q}=boldsymbol{2} boldsymbol{c m} )
7
83Construct a scalene triangle ( boldsymbol{A B C} )
( operatorname{given} A B=3 mathrm{cm}, A C=5 mathrm{cm} ) and
( B C=4 mathrm{cm} )
7
84Complete the following, so as to make a
true statement:
8
855.
5.
IfAB=5 cm, BC = 4 cm, ZB=90° and opposite sides are
equal, then which of the following figure can be
constructed?
(a) Square
(b) Rectangle
(c) trapezium
(d) Rhombus
8
2. Construct a quadrilateral ABCD in which AB=5.5 cm, AD=4.4 cm, CD=6.5 cm, AC=6.5 cm and BD = 7.1 cm.
Sol. Steps of Construction :
D
8
87Can you think of a triangle in which two
altitudes of the triangle are two of its sides?
7
88The minimum number of dimensions
needed to construct a rectangle is
A .2
B. 3
( c cdot 4 )
D.
8
89Construct a ( triangle A B C ) in which ( B C= )
( mathbf{7} boldsymbol{c m} angle boldsymbol{B}=mathbf{7} mathbf{5}^{boldsymbol{o}} boldsymbol{&} boldsymbol{A} boldsymbol{B}+boldsymbol{A C}=mathbf{1 3} boldsymbol{c m} )
7
90( triangle X Y Z ) in which ( Y Z=5.8 c m, angle= )
( 100^{circ}, angle=40^{circ} ) Draw the perpendicular
from ( boldsymbol{Y} ) to ( boldsymbol{X} boldsymbol{Z} )
7
91Construct a right-angled ( angle A B C ) such
that ( angle B=90^{circ}, A B=8 mathrm{cm} ) and ( A C= )
10 ( c m . ) Find length ( B C )
7
92Using ruler and compasses only, construct an isosceles ( Delta A B C )
in which ( B C=5 mathrm{cm}, A B=A C ) and
( angle B A C=90^{0} ) Locate the point ( P ) such
that:
(i) ( P ) is equidistant from ( B C ) and ( A C )
(ii) ( P ) is equidistant from ( B ) and ( C )
7
935.
Is it possible to construct a rhoumbus ABCD where
AC = 6 cm and BD = 7 cm? Justify your answer.
8
94Construct the Parallelogram HEAR, where
HE=5 cm
EA=6 cm
ZR=850
8
95Construct a quadrilateral ( A B C D ) with
( boldsymbol{A B}=mathbf{5} mathrm{cm}, boldsymbol{B C}=mathbf{9} mathrm{cm}, angle boldsymbol{A}= )
( mathbf{3 0}^{circ}, angle boldsymbol{B}=mathbf{9 0}^{circ}, angle boldsymbol{C}=mathbf{1 5}^{circ} )
8
96Construct a ( triangle A B C, ) when ( B C= )
( mathbf{6 . 2} c boldsymbol{m}, boldsymbol{C A}=mathbf{9 . 0} boldsymbol{c m} ) and ( angle boldsymbol{B}=mathbf{9 0}^{circ} )
7
97Construct a quadrilateral ( A B C D ) such
that ( A B=3 c m, B C=4 c m, angle A= )
( 90^{O}, angle B=65^{circ} ) and ( angle C=110^{circ} )
8
985.
To construct a quadrilateral uniquely, it is necessary to
have the knowledge of a least independent elements.
8
999. Construct a trapezium PQRS in which PQ || SR, PQ = 6.5 cm, QR=4.5 cm, ZP=80° and ZQ = 60°.
Sol. Steps of Construction :
8
1006.
To construct a kite which of the following is necessary?
(a) Two adjacent unequal sides and included diagonal.
(b) Two adjacent equal sides and included diagonal.
(C) Opposite sides length.
(d) None of these.
8
101Draw the square ABCD of area 9 square
centimetres.
8
102Construct a triangle ( P Q R ) in which
( Q R=4.8 c m, angle Q=45^{circ} ) and ( angle R=55^{circ} )
7
103Construct a ( triangle A B C ) such that ( A B=7 mathrm{cm} )
( A C=6 mathrm{cm}, B C=9 mathrm{cm} ) measure
( angle A, angle B a n d angle C )
7
1042.
Construct a quadrilateral BDEF, where DE = 4.5 cm, EF =
3.5 cm, FB=6.5 cm, ZF = 50° and ZE=100°.
m.
8
105Which is the last step in the process?
( A cdot 1 )
B. 2
( c .3 )
D. 4
7
106Construct ( Delta T E N ) such that ( mathrm{TE}=3 mathrm{cm} )
( angle E=90^{circ} ) and ( mathrm{NE}=4 mathrm{cm} )
7
107Construct ( Delta L M N ) in which ( angle N= )
( mathbf{7 3}^{circ}, boldsymbol{L} boldsymbol{N}=mathbf{5 . 7} mathbf{c m}, boldsymbol{M} mathbf{N}=mathbf{6 . 8 c m} )
7
( boldsymbol{B C}=mathbf{7 . 5} mathrm{cm}, boldsymbol{A C}=mathbf{5 . 8} mathrm{cm}, boldsymbol{A D}=mathbf{3 . 6} )
( mathrm{cm} )
( C D=4.2 mathrm{cm} ) and ( A=120^{circ} )
8
109State the following statement is true or
false

We can construct a quadrilateral if the measurement of four sides and one
diagonal are given.
A. True
B. False

8
1106.
A quadrilateral can be constructed uniquely if its
sides and one diagonal are given
8
111Construct ( triangle A B C ) such that ( A B= )
( 2.5 c m, B C=6 c m ) and ( A C=6.5 c m )
Measure ( angle B )
7
112Construct a right angle triangle whose
hypotenuse is ( 6 mathrm{cm} ) long and one of the
legs is ( 4 mathrm{cm} ) long.
7
113Construct a quadrilateral ( J U M P )
when: ( J U=3.5 mathrm{cm}, U M= )
( mathbf{4} boldsymbol{c m}, boldsymbol{M} boldsymbol{P}=mathbf{5} boldsymbol{c m}, boldsymbol{P} boldsymbol{J}= )
( 4.5 mathrm{cm}, P U=6.5 mathrm{cm} )
8
114Construct a trapezium ( A B C D ) in which ( boldsymbol{A B} | boldsymbol{C D}, boldsymbol{A B}=mathbf{5} boldsymbol{c m}, angle boldsymbol{B}= )
( mathbf{8 0}^{circ}, boldsymbol{B C}=mathbf{4} boldsymbol{c m} ) and ( boldsymbol{A D}=mathbf{4 . 5} boldsymbol{c m} )
8
115Which of the following statement is/are
correct?
A. when its opposite sides are given
B. when its four angles and a side are given
c. when its diagonals are given
D. when its three angles and any two adjacent sides are given
8
116Draw the following triangles and construct circumcircles for them.
In ( triangle A B C, A B=6 c m, B C=7 mathrm{cm} )
and ( angle A=60^{circ} )
7
117For constructing a unique parallelogram lengths of only
two sides should be given.
8
118Which of the given properties of a parallelogram are
necessary to construct it?
(a) Opposite sides of a parallelogram are equal should be
given
(b) Opposite angles of a parallelogram are equal should
be given.
(c) diagonals of parallelogram bisect each other should
be given.
(d) both (a) and (b)
8
119Construct a quadrilateral ( A B C D ) in
which ( boldsymbol{A B}=mathbf{6} mathrm{cm}, boldsymbol{B C}=mathbf{8} mathrm{cm}, boldsymbol{C D}= )
( mathbf{5} mathrm{cm}, boldsymbol{A} boldsymbol{D}=mathbf{4} mathrm{cm} ) and diagonal ( boldsymbol{A} boldsymbol{C}= )
( 4.5 mathrm{cm} )
8
120Construct a triangle, ( triangle A B C ) with ( A B=5, B C=12 ) and ( A C=13 . ) What
is the measure of ( angle A B C )
A ( .90^{circ} )
B. ( 30^{circ} )
( c cdot 40^{circ} )
D. ( 75^{circ} )
7
121(i) Quadrilateral ( A B C D )
( A B=4.5 c m )
( B C=5.5 mathrm{cm} )
( C D=4 c m )
( A D=6 mathrm{cm} )
( A C=7 c m )
(ii) Quadrilateral ( J U M P )
( J U=3.5 c m )
( boldsymbol{U} boldsymbol{M}=boldsymbol{4} boldsymbol{c} boldsymbol{m} )
( M P=5 c m )
( boldsymbol{P J}=mathbf{4 . 5 c m} )
( boldsymbol{P U}=mathbf{6 . 5 c m} )
(iii) Parallelogram ( M O R E )
( boldsymbol{O} boldsymbol{R}=boldsymbol{6} boldsymbol{c m} )
( boldsymbol{R} boldsymbol{E}=mathbf{4 . 5 c m} )
( E O=7.5 mathrm{cm} )
(iv) Rhombus ( B E S T )
( B E=4.5 c m )
( boldsymbol{E T}=mathbf{6} boldsymbol{c m} )
8
122Length of two sides of a ( triangle A B C ) is ( A B=6 mathrm{cm} ) and ( B C=7 mathrm{cm} . ) Then
which of the following can represent the third side of the triangle ? Also, construct the triangle formed by these three sides
A. ( 8 mathrm{cm} )
в. ( 13 mathrm{cm} )
c. ( 14 mathrm{cm} )
D. ( 15 mathrm{cm} )
7
123Construct ( Delta P Q R ) such that, ( m angle P= )
( mathbf{8 0}^{o}, boldsymbol{m} angle boldsymbol{Q}=mathbf{7} 0^{o}, l(boldsymbol{Q} boldsymbol{R})=mathbf{5 . 7} boldsymbol{c m} )
7
124Draw the right triangle whose sides are ( 3 mathrm{cm}, 4 mathrm{cm} ) and ( 5 mathrm{cm} ) and construct its
centroid
7
125Construct a quadrilateral ( A B C D ) with ( A B=2.5 mathrm{cm}, B C=3.5 mathrm{cm}, C D= )
( 4.5 mathrm{cm}, angle A=90^{circ} ) and ( angle B=120^{circ} )
8
126Construct ( Delta A B C ) in which ( A B=4 mathrm{cm} )
( mathrm{BC}=7 mathrm{cm} ) and ( mathrm{CA}=3 mathrm{cm} . ) Which type of
triangle is this?
7
127Construct ( triangle A B C ) with ( B C=7.5 mathrm{cm} ),
( A C=5 mathrm{cm} ) and ( m angle C=60^{circ} . )
7
1287.
Construct a parallelogram ABCD where AB=4.2 cm, AD=3.5 cm and ZA=75º.
Sol. We first draw a rough sketch of the parallelogram ABCD
8
129Two sides of a triangle are ( 12 mathrm{cm} ) and
14 cm. The perimeter of the triangle is
( 36 mathrm{cm} . ) What is the length of third side
7
130In ( triangle A B C, A B=5 c m, B C= )
( mathbf{6} c boldsymbol{m}, boldsymbol{A C}=mathbf{4} boldsymbol{c m} . ) Identify the type of
triangle.
A. Right angled triangle
B. Isosceles triangle
c. Equilateral triangle
D. Scalene triangle
7
1314.
Construct a quadrilateral NEWS in which NE=7 cm, EW
6 cm, N=60°, ZE=110° and ZS=850
8
132Construct a quadrilateral ( boldsymbol{A B C D} )
where ( A B=4 c m, B C=5 c m, C D= )
( 6.5 mathrm{cm} ) and angle ( B=75^{circ} ) and angle
( C=60^{circ} )
8
A rhombus whose diagonals are 5.2 cm and 6.4 cm long.
A narallelogram OKAY where OK -5.5mond A-42
8
1345.
Construct a rectangle PQRS with PQ=6 cm and diagonal
PR=6.6 cm.
8
135Construct a quadrilateral ABCD in which AB = 3.8 cm,
BC=5 cm, CD=5 cm, DA=5.5 cm and AC=8 cm.
d ulateral ABCD in hiel AD
a
8
136The lengths of the sides of some triangles are given, which of them is not a right angled triangle?
( A cdot 5 mathrm{cm}, 12 mathrm{cm}, 13 mathrm{cm} )
B. ( 7 mathrm{cm}, 24 mathrm{cm}, 25 mathrm{cm} )
( mathrm{c} .5 mathrm{cm}, 8 mathrm{cm}, 10 mathrm{cm} )
D. ( 3 mathrm{cm}, 4 mathrm{cm}, 5 mathrm{cm} )
7
137Constant a quadrilateral ( boldsymbol{A B C D} ), where ( A B=4 c m, B C=5 c m, C D=6.5 mathrm{cm} )
and ( angle B=105^{circ} ) and ( angle C=80^{circ} )
8
138Construct a right angle triangle ( A B C ) in
which ( angle B=90^{circ}, A B=5 mathrm{cm} ) and
( boldsymbol{A C}=mathbf{7} boldsymbol{c m} )
7
1391.
2.9 cm, ZA= 70°; ZB=950, ZC=85°.
8
140In the figure, ( A B C D ) is a quadrilateral.
Name a pair of opposite angles.
8
1414.
In the diagram, KLMN is a constructed parallelogram.
N*
KM
Find the value of ZKLM.
8
142For construction of a ( triangle P Q R, ) where
( Q R=6 mathrm{cm}, P R=10 mathrm{cm} ) and ( angle Q= )
( 90^{circ}, ) its steps for construction is given
below in jumbled form. Identify the first step from the following.
1. At point ( Q ), draw an angle of ( 90^{circ} )
2. From ( R ) cut an arc of length ( P R= )
( 10.0 mathrm{cm} ) using a compass.
3. Name the point of intersection of the
( operatorname{arm} ) of the angle ( 90^{circ} ) and the arc drawn
in step ( 3, ) as ( P )
4. Join ( P ) to ( Q . P Q R ) is the required
triangle.
5. Draw the base side ( Q R=6 mathrm{cm} )
( A cdot 2 )
B. 1
( c cdot 3 )
D. 5
E. 4
7
143Construct a quadrilateral ABCD in which ( A B=3.8 mathrm{cm}, mathrm{BC}=3.4 mathrm{cm}, mathrm{CD}=4.5 )
( mathrm{cm}, mathrm{AD}=5 mathrm{cm} ) and ( angle mathrm{B}=80^{circ} )
8
1443.
The construction of which figure is shown in the diagram?
H
8
145Construct a triangle with perimeter
( 12 c m ) and the ratio of their angles is 3:
4: 5
7
( operatorname{given} P Q=5 mathrm{cm}, Q R=4 mathrm{cm} )
( angle Q P R=35^{circ} ) and ( angle P R S=70^{circ} )
8
147Draw a rough sketch of a quadrilateral
KLMN. State two pairs of opposite sides
8
1483.
Construct a rectangle whose side is 3 cm and a diagonal
equal to 5 cm.
8
149Draw a triangle ( A B C ) in which ( A B=5 mathrm{cm} )
( mathrm{BC}=7 mathrm{cm}, ) and ( angle B=75^{circ} )
7
1500. (-2,4),(4,8),(10,7) and (11,-5) are the
vertices of a quadrilateral. Show that the quadrilateral, obtained on joining the mid-points of its sides, is a parallelogram.
8
151The length of side ( boldsymbol{P S}= )
A. ( 4.2 mathrm{cm} )
в. ( 6.7 mathrm{cm} )
c. ( 5.1 mathrm{cm} )
D. ( 3.5 mathrm{cm} )
8
1521.
BC=CD=7 cm and BD=6 cm. What type of quadrilateral
is this?
8
1537.
Aparallelogram OKAY where OK=5.5 cm and KA=4.2 cm.
Is it unique?
8
154Construct a quadrilateral ( R E A D, ) when
( boldsymbol{R} boldsymbol{E}=mathbf{3 . 5 1} mathrm{cm}, boldsymbol{E} boldsymbol{A}=mathbf{4 . 3} mathrm{cm}, boldsymbol{A D}= )
( 4.8 mathrm{cm}, angle E=105^{circ} & angle R=55^{circ} )
8
155Draw a rough sketch of a regular hexagon. Connecting any three of the draw a triangle. Identify the type of the triangle you have drawn.8
1564.
IfAB = 7.3 cm, one angle is 60° and diagonal bisect each
other at 90°, then which figure can be constructed?
8
157Construct a triangle ( P Q R ) in which ( boldsymbol{P Q}=mathbf{5 . 4 c m}, boldsymbol{Q} boldsymbol{R}=mathbf{5 . 5 c m} ) and
( angle P Q R=55^{circ} )
7
158Draw a triangle ( A B C ) in which ( A B=4.5 )
( mathrm{cm}, mathrm{BC}=6 mathrm{cm} ) and ( angle B=80^{circ} )
7
( boldsymbol{L} boldsymbol{A}=mathbf{6 . 5} boldsymbol{c m} )
( angle P=90^{circ} )
( angle A=110^{circ} )
( angle N=85^{circ} )
8
160For construction of a quadrilateral ( A B C D, ) where ( A B=4.2 mathrm{cm}, B C=3.8 )
( mathrm{cm}, C D=4.9 mathrm{cm}, A D=5.4 mathrm{cm} ) and
( angle B=72 . ) Its steps for construction is
given injumbled form. Identify the first step from the following:
1) From ( B ), set off ( B C=3.8 mathrm{cm} )
2) Draw ( A B=4.2 mathrm{cm} ) and Make
( angle A B X=72^{circ} )
3) With ( A ) as center and radius equal to
( mathbf{5 . 4} mathrm{cm} ) draw an arc.
4) With ( C ) as center and radius equal to ( 4.9 mathrm{cm}, ) draw another arc, cutting the previous arc at ( D . ) Join ( A D ) and ( C D )
( A )
в. 3
( c cdot 4 )
( D )
8
161Construct ( triangle A B C ) such that ( A B= )
( mathbf{2 . 5} mathbf{c m}, boldsymbol{B C}=mathbf{6} boldsymbol{c m} ) and ( boldsymbol{A} boldsymbol{C}=mathbf{6 . 5} boldsymbol{c m} )
Measure ( angle B )
7
162Complete the following, so as to make a
true statement:
8
163( boldsymbol{m} angle boldsymbol{P} boldsymbol{Q} boldsymbol{R}= )
A ( .65^{circ} )
B. ( 79^{circ} )
( c cdot 72 )
D. ( 89^{circ} )
8
164ungo5
.
3.
Which of the following is true for constructing a
(a) 5 sides and 3 diagonals
(6) 3 sides only
(c) 3 angles and their 2 included sides
od 2 diagonals only
8
1652.
Construct a trapezium ABCD in which AB | DC,ZA= 105°,
AD=3 cm, AB=4 cm and CD=8 cm.
8
166Which of the following options is/ are true about a
trapezium to construct it?
(a) one pair of opposite sides of a trapezium should be
parallel and unequal should be given
(b) two non-parallel sides length should be given
(c) two equal opposite angles should be given
(d) all of these
8
167Construct a quadrilateral ( P Q R S ) where ( boldsymbol{P Q}=mathbf{4} boldsymbol{c m}, boldsymbol{Q} boldsymbol{R}=boldsymbol{6} boldsymbol{c m}, boldsymbol{R} boldsymbol{S}= )
( mathbf{5} c m cdot boldsymbol{P} boldsymbol{S}=mathbf{5} . mathbf{5} boldsymbol{c m} ) and ( boldsymbol{P} boldsymbol{R}=mathbf{7} boldsymbol{c m} )
8
1686. Construct a kite ABCD in which AB =4 cm, AD=6 cm and AC=5 cm.
WT
8
169Construct ( triangle A B C ) in which ( B C= )
( mathbf{7} c boldsymbol{m}, angle boldsymbol{B}=mathbf{7} mathbf{5}^{boldsymbol{o}} ) and ( boldsymbol{A} boldsymbol{B}+boldsymbol{A} boldsymbol{C}= )
( 12 mathrm{cm} )
7
DE=4 cm
EA=5 cm
AR=4.5 cm
ZE=60°
ZA=90°
8
171Construct a ( triangle A B C ) in which ( A B= )
( 5 mathrm{cm}, B C=6 mathrm{cm} ) and ( C A=7 mathrm{m} )
7
( angle A=90^{circ}, A B=4.6 mathrm{cm}, B C=5.0 mathrm{cm}, mathrm{AD} )
( =6.0 mathrm{cm} ) and ( mathrm{CD}=4.2 mathrm{cm} )
8
173For construction of a quadrilateral ( A B C D, ) where ( A B=4.2 mathrm{cm}, B C=3.8 )
( mathrm{cm}, C D=4.9 mathrm{cm}, A D=5.4 mathrm{cm} ) and
( angle B=72, ) its steps for construction is given injumbled form. Identify the third step from the following
1) From ( B ), set off ( B C=3.8 mathrm{cm} )
2) Draw ( A B=4.2 mathrm{cm} ) and : Make
( angle A B X=72 )
3) With ( A ) as center and radius equal to
( 5.4 mathrm{cm} ) draw an arc.
4) With ( C ) as center and radius equal to
( 4.9 mathrm{cm}, ) draw another arc, cutting the previous arc at ( D ). Join ( A D ) and ( C D )
A. 3
в.
( c )
D.
8
174Construct a quadrilateral ABCD with Four sides ( : A B=3 mathrm{cm}, mathrm{BC}=4 mathrm{cm}, mathrm{CD} )
( =4.5 mathrm{cm} ) and ( mathrm{AD}=3.8 mathrm{cm} ; angle A B C=90^{0} )
8
175Draw a rough sketch of a quadrilateral KLMN. State two pairs of opposite
angles.
8
176Draw a triangle ( A B C ) with side ( B C=6 )
( mathrm{cm}, angle C=30^{circ} ) and ( angle A=105^{circ} ).Then
construct another triangle whose sides ( operatorname{are} frac{2}{3} ) times the corresponding sides of
( Delta A B C )
7
177To construct a convex quadrilateral, which of the following
cases is not correct?
(a) When the lengths of four sides and one diagonal are
given.
When the lengths of three sides and the two diagonals
are given.
(c) When the lengths of four sides and one angle are
given.
(d) When the lengths of two sides and two included
angles are given.
8
178Construct a right angled ( triangle A B C ) with
( angle B=90^{circ}, B C=5 c m ) and ( A C= )
( 10 mathrm{cm} ) and find the the length of side
( A B )
( mathbf{A} cdot 6.2 mathrm{cm} )
B. ( 5 mathrm{cm} )
( c .8 .7 mathrm{cm} )
D. ( 7.2 mathrm{cm} )
7
179Construct a triangle ( P Q R ) in which
( Q R=7 c m, angle Q=75^{circ} ) and ( P Q+ )
( boldsymbol{P R}=13 mathrm{cm} )
7
1802.
Construct a quadrilateral ABCD in which AB = 5 cm,
AC = 6 cm, AD=8 cm and ZABC = ZACD=90°.
8
181The equation of the diagonal through origin of the quadrilateral formed by the ( operatorname{lines} boldsymbol{X}=mathbf{0}, boldsymbol{Y}=mathbf{0}, boldsymbol{X}+boldsymbol{Y}-mathbf{1}=mathbf{0} )
and ( 6 x+Y-3=0 ) is :
A ( .4 x-3 y=0 )
В. ( 3 x-2 y=0 )
c. ( x=y )
D. ( x+y=0 )
8
182Construct a quadrilateral ( A B C D, ) when
( A B=3.2 mathrm{cm}, B C=5.2 mathrm{cm}, C D=6.2 )
( mathbf{c m}, boldsymbol{D} boldsymbol{A}=mathbf{4 . 2} mathbf{c m} ) and ( boldsymbol{B} boldsymbol{D}=mathbf{5} . boldsymbol{2} mathrm{cm} )
8
183Construct a quadrilateral ( boldsymbol{P} boldsymbol{N} boldsymbol{K} boldsymbol{J} )
where ( mathrm{PN}=7 mathrm{cm}, mathrm{NK}=8 mathrm{cm}, mathrm{JK}=10 mathrm{cm} )
( P J=5 mathrm{cm} ) and ( angle J=75^{circ} )
Then, the measure of ( angle N ) is
A . ( 65^{circ} )
B. ( 95^{circ} )
( c cdot 75^{circ} )
D. ( 85^{circ} )
8
184Construct a ( triangle A B C ) in which ( B C= )
( 4.5 mathrm{cm}, angle B=45^{circ} ) and ( A B+A C=8 mathrm{cm} )
7
185Construct a triangle ( A B C ) in which
( A B=5 c m, B C=4.3 c m ) and ( A C= )
( 4 c m )
7
186Is it possible to construct a triangle
with lengths of its sides as ( 4 mathrm{cm} .3 mathrm{cm} )
7
187Construct a quadrilateral ( A B C D ) in
which ( A B=4.2 c m, B C= )
( 6 c m, C D=5.2 c m, D A=5 c m ) and
( boldsymbol{A C}=mathbf{8 c m} )
8
188Is it possible to have a triangle with the
following sides ( 2 mathrm{cm}, 3 mathrm{cm}, 5 mathrm{cm} )
7
which of the following cases is not
correct?
A. When the lengths of four sides and one diagonal are given
B. When the lengths of three sides and the two diagonals are given
C. When the lengths of four sides and one angle are given
D. When the lengths of two sides and two included angles are given
8
190Construct a quadrilateral ( A B C D ) in
which ( boldsymbol{A B}=mathbf{4 c m}, boldsymbol{B C}= )
( mathbf{3 . 1 c m}, boldsymbol{C D}=mathbf{3} c boldsymbol{m} . boldsymbol{A D}=mathbf{4 . 2 c m} ) and
( A C=5 c m ? ) measure the diagonal ( B D )
( ? )
8
191Using ruler and compasses only, construct a ( triangle A B C ) having given
( angle A B C=60^{0}, angle A C B=45^{0} ) and the
perpendicular from ( boldsymbol{A} ) to ( boldsymbol{B} boldsymbol{C} ) equal to
( 2.5 mathrm{cm} . ) The length of ( A B ) is
A ( .2 .1 mathrm{cm} )
B. ( 2.9 mathrm{cm} )
( c .3 .5 mathrm{cm} )
D. ( 4.2 mathrm{cm} )
7
192Construct a triangle ( A B C ), given the
following ( A B=6 c m, B C=5 c m ) and ( C A= )
( mathbf{5} c boldsymbol{m} )
7
193Complete the following, so as to make a
true statement:

The number of pairs of opposite angles of a quadrilateral is

8
194Using ruler and compasses only, construct a triangle ( A B C ). having ( A B=47 )
( mathrm{cm}, mathrm{AC}=34 mathrm{cm} ) and ( angle B A C=75^{circ} . ) Draw
the perpendicular bisector of BC and the bisector of angle BAC. If the perpendicular bisector and the angle bisector meet at a point ( mathrm{M} ), measure
( angle B M C )
7

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