Converse of Basic Proportionality Theorem
If a line divides two sides of a triangle in the same ratio,
then the line is parallel to the third side.
A
B
C
D
E
l
AD
DB
AE
EC
=
In ΔABC,
∴ line l || side BC
[By converse of B.P.T]
E and F are points on the sides PQ and PR respectively of a ΔPQR.
For each of the following cases, state whether EF II QR :
PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm.
EXERCISE 6.2 - 2(i)
Q
R
P
…(i)
=
=
=
PE
EQ
3.9
3
PE
EQ
39
30
PE
EQ
13
10
∴
E
F
13
10
Hint :
To Check !
PE
EQ
=
PF
FR
Sol.
3.6
2.4
3.9
3
=
PF
FR
3.6
2.4
∴
E and F are points on the sides PQ and PR respectively of a ΔPQR.
For each of the following cases, state whether EF II QR :
PE = 3.9 cm, EQ = 3 cm, PF = 3.6 cm and FR = 2.4 cm.
In ΔPQR,
∴ Line EF is not parallel to side QR
Q
R
P
…(ii)
=
=
=
[From (i) and (ii)]
PF
FR
3.6
2.4
PF
FR
36
24
PF
FR
3
2
∴
≠
PE
EQ
PF
FR
E
F
3
2
Hint :
To Check !
PE
EQ
=
PF
FR
Sol.
3.6
2.4
3.9
3
EXERCISE 6.2 - 2(i)