$D$ and $E$ are points on the sides $A B$ and $A C$ respectively of a $Δ A B C$ . In each of the following cases, determine whether $D E | | B C$ or not. $A D = 7.2 cm, A E = 6.4 cm, A B = 12 cm$ and $A C = 10 cm$ .

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Solution

Given : $A D = 7.2 cm, A E = 6.4 cm, A B = 12 cm$ and $A C = 10 cm$ .

$D B = A B - A D = 12 - 7.2 = 4.8 cm$
$E C = A C - A E = 10 - 6, 4 = 3.6 cm$
$\frac{A D}{D B} = \frac{7.2}{4.8} = \frac{3}{2}$ and
$\frac{A E}{E C} = \frac{6.4}{3.6} = \frac{16}{9}$
$\Rightarrow \frac{A D}{D B} \neq \frac{A E}{E C}$
By the converse of the basic proportionality theorem
$\Rightarrow D E$ is not parallel to $B C$

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Similar questions

Q. D and E are points on the sides AB and AC respectively of a

∆ A B C

. In each of the following cases, determine whether

D E ∥ B C

or not.

(i)

A D = 5.7 cm, D B = 9.5 cm, B D = 4.8 cm and E C = 8 cm .

(ii)

A B = 11.7 cm, A C = 11.2 cm, B D = 6.5 cm and A E = 4.2 cm .

(iii)

A B = 10.8 cm, A D = 6.3 cm, A C = 9.6 cm and E C = 4 cm .

(iv)

A D = 7.2 cm, A E = 6.4 cm, A B = 12 cm and A C = 10 cm .

D and E are points on the sides AB and AC respectively of a $Δ A B C$ . In each of the follwing cases, determine whether DE || BC or not.

(i) AD = 5.7 cm, DB = 9.5 cm, AE = 4.8 cm and EC = 8 cm.

(ii) AB = 11.7 cm, AC = 11.2 cm, BD = 6.5 cm and AE = 4.2 cm.

(iii) AB = 10.8 cm, AD = 6.3 cm, AC = 9.6 cm and EC = 4 cm.

(iv) AD = 7.2 cm, AE = 6.4 cm, AB = 12 cm and AC = 10 cm.

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.

If D and E are respectively the midpoints of the sides AB and BC of $Δ A B C$ in which AB = 7.2 cm, BC = 9.8 cm and AC = 3.6 cm then determine the length of DE.