In , points and are taken on sides and respectively such that and . (i) Show that .…

MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles

Problem

\triangle ABC

, points

D

and

E

are taken on sides

AB

and

AC

respectively such that

\angle ADE = \angle ABC

and

\angle AED = \angle ACB

. (i) Show that

DE \parallel BC

. (ii) Prove that

\triangle ADE \sim \triangle ABC

. (iii) Hence, obtain the relation

\dfrac{DE}{BC} = \dfrac{AD}{AB}

. (iv) If

AD = 3\text{ cm}

AB = 5\text{ cm}

and

BC = 7\text{ cm}

, find the length of

DE