Find the angles respectively of a ∆PQR. For each of the following cases, state whether EF || QR: (i) PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm (ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm (iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.36 cm
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Explanation:
E and F are two points on side PQ and PR in △PQR.
(i) PE=3.9 cm, EQ=3 cm and PF=3.6 cm, FR=2.4 cm
Using Basic proportionality theorem,
∴
EQ
PE
=
3
3.9
=
30
39
=
10
13
=1.3
FR
PF
=
2.4
3.6
=
24
36
=
2
3
=1.5
EQ
PE
=
FR
PF
So, EF is not parallel to QR.
(ii) PE=4 cm, QE=4.5 cm, PF=8 cm, RF=9 cm
Using Basic proportionality theorem,
∴
QE
PE
=
4.5
4
=
45
40
=
9
8
RF
PF
=
9
8
QE
PE
=
RF
PF
So, EF is parallel to QR.
(iii) PQ=1.28 cm, PR=2.56 cm, PE=0.18 cm, PF=0.36 cm
Using Basic proportionality theorem,
EQ=PQ−PE=1.28−0.18=1.10 cm
FR=PR−PF=2.56−0.36=2.20 cm
EQ
PE
=
1.10
0.18
=
110
18
=
55
9
... (i)
FR
PE
=
2.20
0.36
=
220
36
=
55
9
... (ii)
∴
EQ
PE
=
FR.
PF
So, EF is parallel to QR.
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