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Similarity of Triangles

In triangle A...

Question

In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then .

DE = BD

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∠ADE = ∠ACB

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AE = AD

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DE || BC

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Solution

The correct option is D DE || BC

$Given : A B = 18 c m, A D = 8 c m, A E = 12 c m and E C = 15 c m$

$∴ D B = A B - A D = 18 - 8 = 10 cm$

$Now, \frac{A D}{D B} = \frac{8}{10} = \frac{4}{5}$

$and \frac{A E}{E C} = \frac{12}{15} = \frac{4}{5}$

$∵ \frac{A D}{D B} = \frac{A E}{E C}$

$∴ D E ∥ B C (By converse of basic proportionality theorem)$

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Similar questions

In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then which of the following conditions is/are true?

D

and

E

are respectively the points on the sides

A B

and

A C

of a

△ A B C

such that

A B = 12 cm,

A D = 8 cm,

A E = 12 cm

and

A C = 18 cm

, then

Q. In a triangle ABC, D and E are points on sides AB and AC respectively such that, DE||BC. Then

\frac{A D}{A B}

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

Q. In a ∆ABC, D and E are points on the sides AB and AC respectively. For each of the following cases show that DE || BC :

(i) AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm.
(ii) AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 and AE = 1.8 cm.
(iii) AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.
(iv) AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm

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In triangle ABC, D and E are the points on sides AB and AC respectively. If AB = 18 cm, AD = 8 cm, AE = 12 cm and EC = 15 cm, then .

The correct option is D DE || BC Given : AB=18 cm,AD=8 cm,AE=12 cm and EC=15 cm ∴DB=AB−AD=18−8=10 cm Now, ADDB=810 = 45 and AEEC=1215=45 ∵ADDB = AEEC ∴DE∥BC (By converse of basic proportionality theorem)