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Standard X

Mathematics

Similarity of Triangles

D and E are...

Question

$D$ and $E$ are points on the sides $A B$ and $A C$ respectively of $△ A B C$ . For the following case, state whether $D E ∥ B C$ :

$A B = 5.6 c m, A D = 1.4 c m, A C = 9.6 c m$ and $E C = 2.4 c m$

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Solution

The correct option is A No
Given: AB = 5.6 cm, AD = 1.4 cm, AC = 9.6 cm and EC = 2.4 cm

$\frac{A D}{B D} = \frac{A D}{A B - A D} = \frac{1.4}{4.2} = \frac{1}{3}$
$\frac{A E}{E C} = \frac{A C - E C}{E C} = \frac{7.2}{2.4} = 3$
Since, $\frac{A D}{B D} \neq \frac{A E}{E C}$
By converse of equal Intercept theorem, DE is not parallel to BC

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Similar questions

D

and

E

are points on the sides

A B

and

A C

respectively of

△ A B C

. For the following case, state whether

D E ∥ B C

A B = 10.8 c m, A D = 4.5 c m, A C = 4.8 c m

and

A E = 2.8 c m

Q. In a

△

A B C, D

and

E

are points on the sides AB and AC respectively. For each of the following cases show that

D E

∥

B C

(i)

A B = 12 c m, A D = 8 c m, A E = 12 c m a n d A C = 18 c m

(ii)

A B = 5.6 c m, A D = 1.4 c m, A C = 7.2 c m a n d A E = 1.8 c m

(iii)

A B = 10.8 c m, B D = 4.5 c m, A C = 4.8 c m a n d A E = 2.8 c m

(iv)

A D = 5.7 c m, B D = 9.5 c m, A E = 3.3 c m a n d E C = 5.5 c m .

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 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 a

△ A B C, D

and

E

are points on the sides

A B

and

A C

respectively such that

D E ∥ B C

. If

A D = 2.4 c m, A E = 3.2 c m, D E ∥ B C

. If

A D = 2.4 c m, A E = 3.2 c m, D E = 2 c m

and

B C = 5 c m

, find

B D

and

C E

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D and E are points on the sides AB and AC respectively of △ABC. For the following case, state whether DE∥BC:AB=5.6cm,AD=1.4cm,AC=9.6cm and EC=2.4cm

The correct option is A NoGiven: AB = 5.6 cm, AD = 1.4 cm, AC = 9.6 cm and EC = 2.4 cmADBD=ADAB−AD=1.44.2=13AEEC=AC−ECEC=7.22.4=3Since, ADBD≠AEECBy converse of equal Intercept theorem, DE is not parallel to BC

$D$ and $E$ are points on the sides $A B$ and $A C$ respectively of $△ A B C$ . For the following case, state whether $D E ∥ B C$ :

$A B = 5.6 c m, A D = 1.4 c m, A C = 9.6 c m$ and $E C = 2.4 c m$