D and E are points on the sides AB and AC respectively of ΔABC. For each of the following cases, state whether DE ∥ BC :
(i) AD = 5.7 cm, BD = 9.5 cm, AE = 3.6 cm and EC = 6 cm.
(ii) AB = 5.6 cm, AD = 1.4 cm, AC = 9.6 cm and EC = 2.4 cm.
(iii) AB = 11.7 cm, BD = 5.2 cm, AE = 4.4 cm and AC = 9.9 cm.
(iv) AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.

Question

D and E are points on the sides AB and AC respectively of ΔABC. For each of the following cases, state whether DE ∥ BC :
(i) AD = 5.7 cm, BD = 9.5 cm, AE = 3.6 cm and EC = 6 cm.
(ii) AB = 5.6 cm, AD = 1.4 cm, AC = 9.6 cm and EC = 2.4 cm.
(iii) AB = 11.7 cm, BD = 5.2 cm, AE = 4.4 cm and AC = 9.9 cm.
(iv) AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.

KnowledgeBoat · Accepted Answer

By basic proportionality theorem, A line drawn parallel to a side of triangle divides the other two sides proportionally. (i) Given, AD = 5.7 cm BD = 9.5 cm AE = 3.6 cm EC = 6 cm. Check for proportionality, We conclude that DE is parallel to BC Hence, DE is parallel to BC. (ii) Given, AB = 5.6 cm AD = 1.4 cm AC = 9.6 cm EC = 2.4 cm. From figure, DB = AB - AD = 5.6 - 1.4 = 4.2 cm AE = AC - EC = 9.6 - 2.4 = 7.2 cm Check for proportionality, We conclude that DE is not parallel to BC Hence, DE is not parallel to BC. (iii) Given, AB = 11.7 cm BD = 5.2 cm AE = 4.4 cm AC = 9.9 cm. From figure, AD = AB - BD = 11.7 - 5.2 = 6.5 cm EC = AC - AE = 9.9 - 4.4 = 5.5 cm Check for proportionality, We conclude that DE is not parallel to BC Hence, DE is not parallel to BC. (iv) Given, AB = 10.8 cm BD = 4.5 cm AC = 4.8 cm AE = 2.8 cm. AD = AB - BD = 10.8 - 4.5 = 6.3 cm EC = AC - AE = 4.8 - 2.8 = 2 cm Check for proportionality, We conclude that DE is parallel to BC Hence, DE is parallel to BC.

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