i. solve with care: 6 x 3 = 18 · 2017-12-06 · 1. in the given figure (1), in abc, de bc so that...
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TEST - TRIANGLE
I. Solve with care: 6 x 3 = 18
1. In an equilateral triangle with side a, prove that area of the triangle =
a2.
2. State and prove B.P.T Theorem (or) Converse of B.P.T Theorem
3. State and prove Pythagoras theorem.
4. State and prove 2 triangles are similar by using SSS criteria (or) State and
prove 2 triangles are similar by using SAS criteria
5. Prove that the area of an equilateral triangle described on one side of a
square is equal to half the area of an equilateral triangle described on one of
its diagonals.
6. Prove that the sum of the squares on the sides of a rhombus is equal to the
sum of the squares on its diagonals.
7. In triangle PQR and MST, P=55 , Q=25 , M=100 and =25 . Is
QPR TSM? Y (2Marks)
I. Solve with care: 6 x 3 = 18
1. In an equilateral triangle with side a, prove that area of the triangle =
a
2.
2. State and prove B.P.T Theorem (or) Converse of B.P.T Theorem
3. State and prove Pythagoras theorem.
4. State and prove 2 triangles are similar by using SSS criteria (or) State and prove 2
triangles are similar by using SAS criteria
5. Prove that the area of an equilateral triangle described on one side of a square is equal
to half the area of an equilateral triangle described on one of its diagonals.
6. Prove that the sum of the squares on the sides of a rhombus is equal to the sum of the
squares on its diagonals.
7. In triangle PQR and MST, P=55 , Q=25 , M=100 and =25 . Is QPR
TSM? Y (2Marks)
GRADE: X WORKSHEET – TRIANGLE (R.S)
Solve this & Keep your answers in my packet
1. In the given figure (1), in ABC, DE BC so that AD= 4x-3 cm,
AE = 8x-7 cm, BD= 3x-1 cm and CE= 5x-3 cm. Find the value of x.
2. In the figure(2), PQ AB and PR AC. Prove that QR BC.
3. In the figure(3), DE AC and DF AE. Prove that
=
4. In the given fig(4), PA,QB and RC each is perpendicular to
AC such that PA=x, RC=y, QB=z, AB=a and BC=b. Prove that
+
=
5. The diagonals of a quadrilateral ABCD intersect each other at the point
O. such that
=
.
6. In ABC , AD Is a median and E is the midpoint of AD. If BE is
produced , it meets AC in F. Show that AF=
AC.
7. The perimeters of two similar triangles are 25cm and 15cm respectively.
If one side of the first triangle is 9cm, find the corresponding side of
the second triangle.
8. Through the midpoint M of the side CD of a parallelogram ABCD, the
line BM is drawn, intersecting AC in L and AD produced in E. Prove
that EL=2BL.
9. Prove that the area of an equilateral triangle described on one side of a
square is equal to half the area of an equilateral triangle described on
one of its diagonals.
10. Prove that the sum of the squares on the sides of a rhombus is
equal to the sum of the squares on its diagonals.
11. ABC is a right triangle in which = 90 and CD AB.
If BC = a, CA = b, AB = c and CD = p then prove that
(i) cp=ab (ii)
=
+
12. In an equilateral triangle with side a , prove that area =
a2
I. Do match, Don’t scratch :
Column I Column II
1. In a given ABC, DE BC and
=
. If AC = 5.6 cm, then AE = -------cm. 6
2. If ABC DEF such that 2AB=3DE and BC=6cm, then EF = ------cm 4
3. If ABC PQR such that ar( ABC) : ( PQR) = 9:16 and BC = 4.5cm, then QR =-------- cm. 3
4. In a quadrilateral, AB CD and OA = (2x+4)cm, OB = (9x-21)cm, OC = (2x-1)cm and
OD =3cm. Then x = -----
2.1
5. A man goes 10m due east and then 20m due to north. His distance from the starting point
is ------m.
25
6. In an equilateral triangle with each side 10cm, the altitude is ----- cm. 5
7. The area of an equilateral triangle having each side 10cm is ------ cm2 10
8. the length of diagonal of a rectangle having length 8m and breadth 6m is ----m 10
II. MCQ based on synthesis :
1. Look at the statement below:
I. ABC DEF and the altitude of these triangles are in the ratio 1:2, then DEF) = 1:4
II. In ABC DE BC and AD:DB = 1:2, then
=
.
III. In a ABC, P and Q are points on AB and AC respectively such that AP = 3cm, PB=6cm, AQ = 5cm and
QC =10cm, then BC = 3PQ.
Which is true ?
(a) I only (b) II only (c) I and II (d) I and III
Daily Calender
GRADE: X WORKSHEET - TRIANGLE
Save your Date:
1. It is given that FED STU. Is it true to say that
=
?
2. Two sides and the perimeter of one triangle are respectively three times the corresponding
sides and the perimeter of the other triangle; Can you say that the two triangles are similar? Y
3. In triangle PQR and MST, P=55 , Q=25 , M=100 and =25 . Is QPR TSM? Y
4. In the adjoining figure (1), ABC DEF and their sides are of lengths (in cm) as marked
along them. Find the lengths of the sides of each triangle.
5. In the adjoining figure (2), = , if AB= 6cm, BP = 15cm, and CP = 4cm, then find the
lengths of PD and CD.
6. In the adjoining figure (3), ACB = If AC=8cm and AD =3cm, find BD.
7. In the adjoining figure(4), AB DC. If AC and PQ intersect each other at O, Prove that OA x
CQ = OC x AP.
8. In the adjoin figure (5), 1 = . If NSQ MTR, then prove that PTS PRQ
9. In the adjoin figure(6), l m and line segments AB,CD and EF are concurrent at the point P.
Prove that
=
=
10. Legs (Sides other than the hypotenuse)(fig 7) of a right triangle are of length 16cm and 8cm.
Find the length of the side of the largest square that can be inscribed in the triangle.
I. S
ho
ot
the
bal
loo
n li
ke D
evas
en
a:
4.
Fin
d t
he
max
imu
m v
alu
e
of
cose
c
.
3.
Fo
r an
y t
rian
gle
AB
C ,
fin
d t
he
val
ue
of
cos[
]
.
2.
If s
in[A
+B]=
=
cos[
A-B
] , t
hen
fin
d
the
valu
e o
f [
.
1.
In t
rian
gle
AB
C ,
angl
e B
= 9
0
,
pro
ve t
hat
sin
2A
+sin
2 C=1
.
6.
Pro
ve t
hat
+
=
1+s
ec
7.
Pro
ve t
hat
-
=
-
.
5.
If
, t
hen
pro
ve t
hat
:
.
Bes
t sh
oo
ter
Pri
zes:
1.If
sec
,
pro
ve t
hat
.
2.If
,
and
.
Fin
d v
alu
e o
f (A
+B)
usi
ng
.
3.P
rove
th
at :
Pre
par
e yo
ur
Sho
rt f
ilm
her
e
1. If
tri
an
gle
OC
A ~
tri
an
gle
OD
B, t
hen
pro
ve t
ha
t A
C
pa
ralle
l BD
.
2.In
th
e g
iven
fig
ure
, A
BC
is a
n
equ
. , w
ho
se e
ach
sid
e
mea
sure
s x
un
its.
P a
nd
Q a
re
two
po
ints
on
BC
pro
du
ced
su
ch
that
PB
= B
C =
CQ
. Pro
ve t
hat
:
(a)
PQ
/PA
= P
A/P
B (
b)
PA
2 = 3
x2
3. P
rove
th
at t
he
rati
o o
f th
e
are
as o
f tw
o s
imila
r tr
ian
gles
is
equ
al t
o t
he
squ
are
of
the
rati
o
of
thei
r co
rres
po
nd
ing
med
ian
s.
4.In
an
iso
sce
les
tria
ngl
e, i
f th
e
len
gth
of
its
sid
e a
re A
B=5
cm,
AC
=5cm
,BC
=6cm
,th
en f
ind
th
e
len
gth
of
its
alti
tud
e d
raw
n
fro
m A
on
BC
.
5.Th
ree
sid
es o
f a
tria
ngl
e ar
e
60 m
,50m
an
d 1
20m
. Are
th
ese
sid
es
of
a ri
ght
angl
es
tria
ngl
e?
6.P
rove
th
at in
an
eq
ui
, th
ree
tim
es o
f th
e sq
uar
e o
f o
ne
of
the
sid
es is
eq
ual
to
fo
ur
tim
es
of
the
squ
are
of
on
e o
f it
s al
titu
des
.
7.I
n t
he
fig
ure
, in
tri
an
gle
AB
C,A
D
BC
. Pro
ve
th
at
AC
2=
AB
2+
BC
2-2
BC
.BD
.
8.In
A
BC
, AD
BC
, wh
ere
D li
es
on
BC
. Als
o, B
D=3
CD
.Pro
ve t
hat
2AB
2=2
AC
2+B
C2.
9.D
an
d E
are
po
ints
on
th
e si
de
CA
an
d C
B r
esp
ecti
vely
of
a
AB
C, r
igh
t an
gle
d a
t C
.
Pro
ve t
hat
AE2
+ B
D2 =A
B2 +D
E2.
10.A
BC
is a
n is
osc
ele
s
in
wh
ich
AB
=AC
an
d B
C2 =2
AB
2.
Pro
ve t
hat
AB
C is
a r
igh
t
.
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