KnowledgeBoat Logo

Mathematics

In the figure (ii) given below, ∠D = ∠E and ADDB=AEEC\dfrac{AD}{DB} = \dfrac{AE}{EC}. Prove that ABC is an isosceles triangle.

In the figure (ii) given below, ∠D = ∠E and AD/DB = AE/EC. Prove that ABC is an isosceles triangle. Similarity, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

Similarity

46 Likes

Answer

Given, ∠D = ∠E

So, AD = AE [Sides opposite to equal angles]

Given, ADDB=AEEC[….Eq 1]\dfrac{AD}{DB} = \dfrac{AE}{EC} \qquad \text{[….Eq 1]}

Hence, by basic proportionality theorem, DE is parallel to BC.

As AD = AE so in order to satisfy Eq 1, DB = EC.

AB = AD + DB = AE + EC

and AC = AE + EC.

Hence, AB = AC which means ABC is an isosceles triangle.

Answered By

29 Likes

Related Questions