$E$ and $F$ are points on the sides $P Q$ and $P R$ respectively of a $△ P Q R$ . For each of the following cases, state whether $E F ∥ Q R$ :
$P Q = 1.28 c m, P R = 2.56 c m, P E = 0.18 c m$ and $P F = 0.36 c m$ .

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Solution

$P Q = 1.28$ cm
$P E = 0.18$ cm
$E Q = P Q - P E = 1.28 - 0.18 = 1.1$ cm

$P R = 2.56$ cm
$P F = 0.36$ cm
$F R = P R - P F = 2.56 - 0.36 = 2.20$ cm

$\frac{P E}{E Q} = \frac{1.28}{1.1} = \frac{128}{110}$
$\frac{P F}{F R} = \frac{2.56}{2.2} = \frac{128}{110}$
Since, $\frac{P E}{E Q} = \frac{P F}{F R}$
Hence, by converse of equal intercept theorem, $E F ∥ Q R$

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Similar questions

E and F are points on the sides PQ and PR respectively of a ΔPQR. 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 = 0.63 cm

P Q = 1.28 c m, P R = 2.56 c m, P E = 0.18 c m

and

P F = 0.36 c m

Question 2 (iii)
E and F are points on the sides PQ and PR respectively of a $Δ P Q R$ . For the following case, state whether EF || QR.
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.63 cm

E

and

F

are points on the sides

P Q

and

P R

respectively of a

Δ P Q R

. For each of the following cases state whether

E F ∥ Q R

(1)

P E = 3.9 c m, E Q = 3 c m, P F = 3.6 c m a n d F R = 2.4

(2)

P E = 4 c m, Q E = 4.5 c m, P F = 8 c m a n d R F = 9 c m

(3)

P Q = 1.28 c m PR = 2.56 c m, P E = 0.18 c m a n d P F = 0.36 c m

Question 2 (iii)
E and F are points on the sides PQ and PR respectively of a $Δ P Q R$ . For the following case, state whether EF || QR.
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm and PF = 0.63 cm

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E and F are points on the sides PQ and PR respectively of a △PQR. For each of the following cases, state whether EF∥QR:PQ=1.28 cm,PR=2.56 cm,PE=0.18 cm and PF=0.36 cm.

PQ=1.28 cm PE=0.18 cm EQ=PQ−PE=1.28−0.18=1.1 cm PR=2.56 cm PF=0.36 cm FR=PR−PF=2.56−0.36=2.20 cm PEEQ=1.281.1=128110 PFFR=2.562.2=128110 Since, PEEQ=PFFR Hence, by converse of equal intercept theorem, EF∥QR

$E$ and $F$ are points on the sides $P Q$ and $P R$ respectively of a $△ P Q R$ . For each of the following cases, state whether $E F ∥ Q R$ :
$P Q = 1.28 c m, P R = 2.56 c m, P E = 0.18 c m$ and $P F = 0.36 c m$ .