worksheet ch1

8/15/2019 Worksheet Ch1

http://slidepdf.com/reader/full/worksheet-ch1 1/22

1.

In the diagram below, MNL ABC ∆≡∆

. Find the values of the unknown marked.

Answer: x

= …………………….[1]

y = …………………….[ ]

z = …………………….[1]

2. Find x

and y

if the triangles are !ongruent.



104

2 cm7 cm3 cm

4 cm

12 cm29

?

Answer: x

= …………………….

°

["]

y= …………………!m

[1]

#. In the diagram below, ∆ ABC is similar to ∆ ADE . AE = " !m, BE = # !m, DE = $ !m,

BC = 1" !m, DC = !m, ∠ EAD = 1%$° and ∠ ABC = "&° .

(a) Find ∠ AED,

'b( )al!ulate the length of A*.

Ans: 'a( ∠ AED = ++++++++++++ [1]



PQ

S R

%",

2 cm

5 cmPR

4.5 cm

'b( AD = ++++++++++++ !m ["]1%. In the diagram, PQR and QST are straight lines. It is given that TQ is -er-endi!ular to PR , PT = RS ,

QR = " QS , where S is the mid-oint of QT and.", %=∠QRS

'a( ame a -air of !ongruent triangles .

'b( If the length of QS is "% units, find the ratio PQ : QR.

Ans: 'a( ++++++++++++++++++ [ ]

++++++++++++++++++

'b( ++++++++++++++++++ ["]

1$. /riangles PQR and STR are similar. Find the length of PS .

Ans: !m ["]

Q

S

T



A

C

B

D

T

x °y°

A

B C

P Q

x cm

8 cmy cm

4 cm

6 cm

15 cm

10. /he diagram below shows a uadrilateral ABCD . /he diagonals AC and BD interse!t

at T . AT = BT and CT = DT .

'i( ame a triangle whi!h is !ongruent to triangle ATD . 2ive 3our reasons and

state the !ase of !ongruen!e.

[ ]

'ii( ame a triangle whi!h is similar to triangle CDT . [1]

'iii( 2iven that ∠ DAC = x4 and ∠CAB = y4, e5-ress ∠ ACB in terms of x and y. ["]

'iv( 2iven also that AB = !m, AT = " !m and DB = # !m, !al!ulate the length of

DC .

["]

"%.

In the diagram above, triangle ABC is enlarged to triangle APQ . AC = x !m, AB = $ !m, BP = y !m, CQ = !m, BC = 6 !m and PQ = 10 !m. 7ine BC is -arallel to line PQ .

'a( Find the value of x.'b( Find the value of y.'!( Find the s!ale of enlargement, k , from triangle ABC to triangle APQ .



Ans: 'a( !m ["]

'b( !m ["]

'!( [1]"0. In the diagram, the right8angled triangle A9) is similar to triangle A* , where

A* = & !m, 9* = 6 !m and A) = 0 !m.

Find(i) 9),(ii) area of triangle A* .

A

0 !m

B C

6 !m

D E



Ans: 'i( ++++++++++++++++++++[1]

'ii( ++++++++++++++++++++["]

"6. 5-and ' x ; y(' x < y(. en!e evaluate

("

1"('

"

1"' +−

.

Ans: +++++++++++++++++++++++["]

"#. (a) 5-ress

x x "

1

(1'

" −+

as a single fra!tion in its sim-lest form.

(b) >im-lif3

"

"

("'$ x x y

x xy x −

÷−

.



Ans: 'a( ++++++++++++++++++++++["]

'b( ++++++++++++++++++++++[ ]

".

>olve the following e uations:

'a( x x #$ " =

'b(( )( ) "%0 =−+ x x



7 cm

C

B

A

40º

55º

L

M

N4 cm

3 cmx

'a(. ++++++++++++++++ ["]

'b(. ++++++++++++++++ [ ]"&.

In the diagrams below, triangle ABC is similar to triangle LMN .

Find the unknown angle x and side y marked in the diagrams.

x = ++++++++++++++? [1]

y = ++++++++++++!m ["]%

.>teven bought x /8shirts !osting a total of @1 % from a wholesaler.

'a( rite an e5-ression, in terms of x, the !ost -ri!e of one /8shirt.

'b( If he wants to sell the /8shirts at a -rofit of @ for ea!h /8shirt, write ane5-ression, in terms of x, for the selling -ri!e of ea!h /8shirt.

'!( e sold " /8shirts at a -rofit of @ ea!h while the rest were sold at @#ea!h. rite an e5-ression, in terms of x, for the total amount of mone3 he wouldre!eive for selling all the /8shirts.

'd( If he made a -rofit of @1%% for selling all the /8shirts, form an e uation in

terms of x and show that it redu!es to.%#"%06" =+− x x

["]

(e) en!e find the number of /8shirts >teven bought.

y !m



16

Q

P

A

B

C

12y

20x

6

'a(. @+++++++++++++++++ [1]

'b(. @+++++++++++++++++ [1]

'!(. @+++++++++++++++++ ["]

'e(. +++++++++++ /8shirts ["]1

.In the diagram below, BC is -arallel to 9).

2iven that AC = 6 !m, BC = 1" !m, A9 = "% !m, 9) = 16 !m, AB = x !m and C) = y !m.

'a( ame the -air of similar triangles in the figure'b( Find x and y



'a(. D+++++ similar to D+++++ [1]

'b(. x = +++++++++++++!m ["]

y = ++++++++++++++!m ["]32. >im-lif3 ea!h of the following:

(a)bybxayax

bxax1"10,1%

%"% ""

+++

+



MP

N

Q

R

5 cm

15 cm

9 cm 4 cm

Answer ……………………………["]

(b)"

111$&

1" −

++− x x x

Answer ……………………………["]

. In the figure below,∆

PMN is similar to∆

PQR . Find the value of PN and NQ .

Answer PN = …………………. !m [1]



B

D

3 cm

A E C5 cm 2 cm

NQ = ………………… !m ["]

$. In the figure below,∆

AED is enlarged to∆

ABC . 2iven that ∠ AED = ∠ ABC , AD = !m, AE = 0 !mand EC = " !m, !al!ulate

(a) the s!ale fa!tor of the enlargement.(b) the length of AB.

Answer (a) ……………………… [1]

(b) AB = …………….. !m [1]

0. valuate"

$

11

""" −+

÷−

++ x x

x

x

x

x.



Answer [$]

6. Ift t rs =− "$

, e5-ress t in terms of r and s in its sim-lest form.

Answer [ ]

7. Fa!toriEe the following !om-letel3(a) "111" " −− x x

,

(b) #" y" − 0% x" ,

(c) $ p ' r ; s( < ' p < ( '" s ! " r (.



Answer 'a( [1]

'b( ["]

'!( [ ]

38. >im-lif3 the following algebrai! fra!tions. 7eave 3our answer as a fra!tion whereverne!essar3.

(a)22 " #

b#a" b" a#−

+−− [2]

(b)

ab

ba

ba

ab

−

+[2]

39. Make x the subject of the formula

2

2

5

32

x x

y−

+=

[3]



A

B C

D

E

4 cm

6 cm10 cm

40. Find the two consecuti e ne!ati e odd numbers such that the s"uare of their sum e#ceeds thesum of their s"uares b$ %0. &se ONLY algebraic method to sol e. [5]

In the figure below, ∆ BAC is similar to ∆ CED . 2iven that AC = 1% !m, DE = 6 !m,

AB = $ !m and DCE ∠

= &%o. Find

(a) ∠ ABC (b) the length of EC .(c) DC BC :



A

DB

C

E

5 cm12 cm

13 cm

A

B

C

D

E

F

G

16

21

28

Answer (a) ° [1]

(b) cm [2]

(c) [1]

42. In the diagram below, triangle ABC is !ongruent to triangle DBE , AC = 1 !m, BC = 0 !m and!m. Find the length of

'a( * ,'b( A .

Ans 'a( +++++++++++ !m

'b( +++++++++++ !m$ . In the diagram below 'not drawn to s!ale(, BC is -arallel to DEF , CGE is -arallel to ABD , BD = 16

!m, DF = " !m and BC = "1 !m.(a) ame two triangles whi!h are similar to ∆ BDF . [2]

(b) )al!ulate the lengths of

(i) EG , [2] (ii)

AB . [3]



44. 'a( In the diagram, ∆ $%& and ∆ $QP are similar, P% = $ !m, $% = 1" !m, PQ = "1 !m,

$& = 6 !m and11&=∠ $PQ

. Find

'i( the length of GH, ["]

'ii( the length of CH, ["]

'iii( %&Q∠

.[1]



11&

Y 2

8.7

8.26.5

A

B

C

Z

X

$0. In the diagram, ∆ ABC is !ongruent to ∆ %&' . AB = .# !m, BC = 6.0 !m, C' = ." !m and A& = " !m.Find the length of

'a( A' ,'b( %' .



C

A

B

P

Q

12

6

4

12

Ans: 'a( !m [1]'b( !m [1]

$6.

2iven that"

1

−

+=

p

p

,'i(

e5-ress p

in terms of , giving 3our answer in its sim-lest form.["]

'ii(!al!ulate the value of

p when = 6.

[1]

$#. /he diagram shows triangle A9). BC is -arallel to 9). AC = 1" !m, B9 = 6 !m,C) = $!m and 9) = 1" !m.



'i(Brove that

∆

A9) is similar to∆

ABC.["]

'ii( )al!ulate the length of BC. [1]

'iii( )al!ulate the length of A9. [1]

$ . In the diagram, ∆ ABC is !ongruent to ∆ %&' . /he dimensions given are in !m.Find

'a( the length of AC ,'b( the length of &' ,'!( ∠&%' ,'d( ∠ ACB .


http://slidepdf.com/reader/full/worksheet-ch1 21/22P Q

B C

A

8cm7cm

6cm

x

y

21cm

'a(………………………… [1]'b(………………………… [1]'!(………………………… [1]'d(………………………… ["]

$&. In the diagram, DE is similar to %&' .

Find

'i( %&' ∠

,'ii( the length of D .

Answer

'b( 'i( %&' ∠

= J [1]

'ii( D = !m ["]0%.

2iven that ABC ∆

is similar to APQ∆

, A9 = !m, 9) = 6 !m, A) = # !m,

)C = "1 !m, 9B = x

!m and BC = y

!m, !al!ulate the value of x

and y

.

D

% 1 !m

'

1" !m0J16 !m & E



Ans:= x

+++++++++++!m[ ]

= y

++++++++++ !m

01. In the diagram, A9) and * ) are similar. 2iven that ) = !m, )* = 0 !m

and *9 = " !m, find the length A .

Answer: A =+++++++++++!m [ ]

worksheet ch1

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