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

.

1.

Pro

ve

that

:

2.

Sh

ow

th

at

3.

Pro

ve

that

: 1

+

.

4.

5.

Pro

ve

that

:

6.

=1.

7.

8.

± 2+ 2− 2.

9.

10

.

Do

n’t

pla

y B

lue

wh

ale

(Dan

ger)

Let

us

pla

y m

ath

Wh

ale(

Safe

r)