Question

In Fig. 12.77, it is given that the angle BAD = the angle CAE and the angle B = the angle D, Prove that i) AB/AD =AC/AE ii)the angle ADB =the angle AEC.​

Answer 1

Solution :-

given that,

→ ∠BAD = ∠CAE

adding ∠DAC both sides,

→ ∠BAD + ∠DAC= ∠CAE + ∠DAC

→ ∠BAC = ∠DAE ------- Eqn.(1)

Now, in ∆ABC and ∆ADE we have,

→ ∠ABC = ∠ADE { given }

→ ∠BAC = ∠DAE { From Eqn.(1) }

therefore,

→ ∆ABC ~ ∆ADE { By AA similarity. }

hence,

→ AB/AD = AC/AE { Corresponding sides of similar ∆'s are in proportion. }

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