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In the figure (ii) given below, BD bisects ∠ABC. Prove that ABBD=BEBC\dfrac{AB}{BD} = \dfrac{BE}{BC}.

In the figure (ii) given below, BD bisects ∠ABC. Prove that AB/BD = BE/BC. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

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Answer

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In the figure (ii) given below, BD bisects ∠ABC. Prove that AB/BD = BE/BC. Circles, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

In △ABE and △BCD,

∠A = ∠D (∵ angles in same segment are equal.)

∠ABE = ∠DBC (As BD is bisector of ∠ABC)

△ABE ~ △BCD (AA rule of similarity).

Since, ratio of corresponding sides of similar triangles are equal,

∴ ABBD=BEBC.\dfrac{AB}{BD} = \dfrac{BE}{BC}.

Hence, proved.

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