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Byju's Answer

Standard IX

Mathematics

Application of BPT

D and E are r...

Question

D and E are respectively the points on the sides AB and AC of a $Δ A B C$ such that AB = 5.6 cm. AD = 1.4 cm. AC = 7.2 cm and AE = 1.8 cm. Then, $D E ∥ B C$ .

True

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False

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Solution

The correct option is A
True

We have,

AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm.

Now, $\frac{A D}{D B} = \frac{1.4}{5.6} = \frac{1}{4}$

$\frac{A E}{E C} = \frac{1.8}{7.2} = \frac{1}{4}$

$\Rightarrow \frac{A D}{D B} = \frac{A E}{E C}$

Thus, DE divides sides AB and AC of $Δ A B C$ in the same ratio.

$∴$ By the converse of Basic Proportionality Theorem, we have

$D E ∥ B C$

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Similar questions

D and E are respectively the points on the sides AB and AC of a $Δ A B C$ such that AB = 5.6 cm. AD = 1.4 cm. AC = 7.2 cm and AE = 1.8 cm. Show that $D E ∥ B C$ . [1 MARK]

D and E are respectively the points on the sides AB and AC of a $Δ$ ABC such that AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm, prove that DE || BC.

Q. In given figure

D

and

E

are respectively the points on the sides

A B

and

A C

of a

△ A B C

such that

A B = 5.6 c m, A D = 1.4 c m, A C = 7.2 c m

and

A E = 1.8 c m

. Then show that

D E | | B C

D

and

E

are respectively the points on the sides

A B

and

A C

of a

Δ A B C

such that

A B = 12 c m, A D = 8 c m, A E = 12 c m

and

A C = 18 c m

, show that

D E ∥ B C

In a $Δ A B C$ , D and E are points on the sides AB and AC respectively. For each of the following cases show that DE || BC:
(i) AB = 12cm, AD = 8 cm, AE = 12 cm and AC= 18cm.
(ii)AB = 5.6cm, AD= 1.4cm, AC = 7.2 cm and AE= 1.8 cm.
(iii) AB= 10.8 cm, BD= 4.5cm, AC = 4.8cm and AE =2.8 cm.
(iv)AD = 5.7cm, BD = 9.5cm, AE = 3.3cm and EC = 5.5 cm.

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D and E are respectively the points on the sides AB and AC of a ΔABC such that AB = 5.6 cm. AD = 1.4 cm. AC = 7.2 cm and AE = 1.8 cm. Then, DE∥BC.

The correct option is A True We have, AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm. Now, ADDB=1.45.6=14 AEEC=1.87.2=14 ⇒ADDB=AEEC Thus, DE divides sides AB and AC of ΔABC in the same ratio. ∴ By the converse of Basic Proportionality Theorem, we have DE∥BC

D and E are respectively the points on the sides AB and AC of a $Δ A B C$ such that AB = 5.6 cm. AD = 1.4 cm. AC = 7.2 cm and AE = 1.8 cm. Then, $D E ∥ B C$ .