Iii E and F are points on the sides PQ and PR respectively of a - PQR- 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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Standard X

Mathematics

Basic Proportionality Theorem

iii E and F a...

Question

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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Solution

In ΔPQR, E and F are two points on the sides PQ and PR respectively.
(iii) PQ = 1.28 cm, PR = 2.56 cm, PE = 0.18 cm, PF = 0.36 cm
(Given) Here, EQ = PQ - PE = 1.28 - 0.18 = 1.10 cm;
FR = PR - PF = 2.56 - 0.36 = 2.20 cm
So, $\frac{P E}{E Q} = \frac{0.18}{1.10} = \frac{18}{110} = \frac{9}{55} . . . (i)$
And, $\frac{P E}{F R} = \frac{0.36}{2.20}$ = $\frac{36}{220} = \frac{9}{55} . . . (i i)$
$∴ \frac{P E}{E Q} = \frac{P F}{F R}$ .
Hence, EF is parallel to QR.

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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

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

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

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

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

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Basic Proportionality Theorem

Standard X Mathematics

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Question 2 (iii) E and F are points on the sides PQ and PR respectively of a ΔPQR. 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

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