In , points on and on are chosen such that , , and . (i) Derive the condition on for…

MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles

Problem

\triangle ABC

, points

D

AB

and

E

AC

are chosen such that

AD = (x-2)\text{ cm}

DB = (2x+1)\text{ cm}

AE = (3x-4)\text{ cm}

and

EC = (5x-9)\text{ cm}

. (i) Derive the condition on

x

for which

DE

will be parallel to

BC

. (ii) For the value

x=5

, determine whether

DE

is parallel to

BC

. Show all steps clearly and explain any inconsistency you observe.