Question

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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Answer 1

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.

Answer 2

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