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.

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Solution

$D E | | B C i f △ A D E a n d △ A B C a r e s i m i l a r$

(i) $\frac{A D}{D B}$ = $\frac{5.7}{9.5}$ =0.6

$\frac{A E}{E C}$ = $\frac{4.8}{8}$ =0.6

therefore DE || BC

$i n space increment A B C space a n d space increment A D E space a r e space si m i l i a r space t h e n D E parallel to B C 2 right parenthesis a s s u m e space increment A B C space a n d space increment A D E space a r e space si m i l i a r t h e n fraction numerator A B over denominator A D end fraction equals fraction numerator A C over denominator A E end fraction A D equals A B minus B D equals 11.7 minus 6.5 equals 5.2 fraction numerator 11.7 over denominator 5.2 end fraction equals fraction numerator 11.2 over denominator 4.2 end fraction 2.25 not equal to 2.67 i n space t h i s space c a s e space D E not parallel to B C 3 right parenthesis a s s u m e space increment A B C space a n d space increment A D E space a r e space si m i l i a r t h e n fraction numerator A B over denominator A D end fraction equals fraction numerator A C over denominator A E end fraction A E equals A C minus E C equals 9.6 minus 4 equals 5.6 fraction numerator 10.8 over denominator 6.3 end fraction equals fraction numerator 9.6 over denominator 5.6 end fraction 1.714 equals 1.714 i n space t h i s space c a s e D E parallel to B C 4 right parenthesis a s s u m e space increment A B C space a n d space increment A D E space a r e space si m i l i a r t h e n fraction numerator A B over denominator A D end fraction equals fraction numerator A C over denominator A E end fraction fraction numerator 12 over denominator 7.2 end fraction equals fraction numerator 10 over denominator 6.4 end fraction 1.67 not equal to 1.56 i n space t h i s space c a s e i n space t h i s space c a s e space D E not parallel to B C$

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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 .

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.

Q. In a