Question 2 iiE and F are points on the sides PQ and PR respectively of a - PQR- For the following case- state whether EF QR-ii PE -4 cm - QE -4-5 cm - PF -8 cm and RF -9 cm

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Standard X

Mathematics

Ratio of Area of Similar Triangles

Question 2 ii...

Question

Question 2 (ii)
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.
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm

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Solution

In ΔPQR, E and F are two points on the sides PQ and PR respectively.
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8cm, RF = 9cm
$∴ \frac{P E}{Q E} = \frac{4}{4.5} = \frac{40}{45} = \frac{8}{9}$ [By using Basic proportionality theorem]
And, $\frac{P F}{R F} = \frac{8}{9}$
So, $\frac{P E}{Q E} = \frac{P F}{R F}$
Hence, EF is parallel to QR.

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Similar questions

Q. E and F are points on the side PQ and PR respectively of

△

PQR.For the following case , state whether EF

∥

QR
PE=4 cm , QE=4.5 cm , PF =8 cm and RF= 9 cm

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

Question 2 (ii)
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.
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 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

E

and

F

are the points on the side

P Q

and

P R

respectively of

△ P Q R

. For each of the following cases, state that

E F ∥ Q R

. If True type

1

and for False type

0

P E = 4 c m

Q E = 4.5 c m

P F = 8 c m

and

R F = 9 c m

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Question 2 (ii) E and F are points on the sides PQ and PR respectively of a ΔPQR. For the following case, state whether EF || QR. (ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm

In ΔPQR, E and F are two points on the sides PQ and PR respectively. (ii) PE = 4 cm, QE = 4.5 cm, PF = 8cm, RF = 9cm ∴PEQE=44.5=4045=89 [By using Basic proportionality theorem] And,PFRF=89 So, PEQE=PFRF Hence, EF is parallel to QR.

Question 2 (ii)
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.
(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm