Question

(үті)
3 ст.
2 ст.
5 сі.
(vii)
6 ст.
6 см.
Explain why the triangles are similar and then find the value of x.
2 ст.
PS
В"
4 ст.
R
4.5
(1)
T
5
х
5
В
A70
3
RL​

Answer 1

Answer:

) From figure ( i )

In ∆PQR , ∆LST

<Q = <T ( given )

<R = <S = 90°

Therefore ,

∆PRQ ~ ∆LST ( A.A similarity )

Then ,

QR/ST = PQ/TL

=> 3/4.5 = 5/x

=> 3x = 5 × 4.5

=> x = ( 5 × 4.5 )/3

x = 7.5

_______________________

2 ) from figure ( ii ) ,

In ∆ABC and ∆PQR

<ABC = <PQC = 70°

( corresponding angles )

<C = <C ( common angle )

Therefore ,

∆ABC ~ ∆PQC ( A.A similarity )

then

AB/PQ = BC/QC

=> 5/x = ( BQ + QC )/QC

=> 5/x = ( 3 + 3 )/3

=> 5/x = 2

x = 5/2

x = 2.5

_____________________

3 ) from figure ( iii ) ,

In ∆ABC and ∆DEC

<A = <E ( given )

<BCA = <ECD

( vertically opposite angles )

Therefore ,

∆ABC ~ ∆DEC ( A.A similarity )

then ,

BC/CD = AB/DE

=> 22/x = 24/14

=> 22/x = 12/7

=> x/22 = 7/12

=> x = ( 7 × 22 )/12

x = 77/6 = 12 5/6

______________________

4 ) From figure ( iv )

Given AB//ST

then ,

RA/RS = RB/RT----( 1 )

( Thales theorem )

<RAB = <RST-----( 2 )

( corresponding angles )

From ( 1 ) and ( 2 ),

∆RAB ~ ∆RST

[ SAS similarity ]

RA/RS = RB/RT = AB/ST

RA/RS = AB/ST

6/8 = 9/x

=> x = 12

______________________

5 ) FROM figure ( v ),

In ∆PQR , MN // QR

PM/PQ = PN/PR ( Thales theorem )

<PNM = <PRQ ( corresponding angles )

∆PQR ~ ∆PMN

[ SAS similarity ]

PM/PQ = PN/PR = MN/QR

=> PN/PR = MN/QR

4/( 4 + x ) = 5/15

=> 4/( 4 + x ) = 1/3

x = 8

_____________________

6 ) from figure ( vi )

In ∆XYZ , AB // ZY

XA/XZ = XB/XY ---( 1 )

[ Thales theorem ]

<XAB = <XZY ----( 2 )

[ corresponding angles ]

∆XZY ~ ∆XAB

[ SAS similarity ]

XA/XZ = AB/ZY

=> XA/( XA + AZ ) = AB/ZY

=> x/( x + 7.5 ) = 12/18

=> x/( x + 7.5 ) = 2/3

after simplification ,

x = 15

_________________

7) From figure ( vii )

In ∆ABC , ∆EDC

<ABC = <EDC = 90°

<BCA = <DCE

[ angle of incidence and angle of

reflection are same ]

∆ABC ~ ∆EDC

[ A.A similarity ]

AB/ED = BC/CD

=> 1.6/x = 1.5/15

=> after simplification

x = 16

______________________

8 ) From figure viii

Data not sufficient .

______________________

Step-by-step explanation: