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7. In the fig.4.141 given, DE ∥ BC such that . If , find AD.

Solution:

Given:

DE∥BC

.

To find: AD.

In ΔADE and ΔABC

∠A = ∠A (Common)

(Corresponding angles as AB||QR with PQ as the transversal)

∠ADE = ∠ABC

(By AA similarity criteria)

⇒ ΔADE  ΔABC

(Corresponding Parts of Similar Triangles are propositional)

AD/AB = AE/ AC