Question

# In a ΔABC, 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.

Solution

## DE will be || to BC when   ( it shows that ABC and ADE are similar triangles with common angle A, Hence the other two corresponding angles will be equal too) (i)      Hence DE|| BC (ii)                Hence  DE|| BC (iii)                 Hence  DE|| BC (iv)                Hence  DE|| BC MathematicsRD SharmaStandard X

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