In a triangle

MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles

Problem

In a triangle

ABC

, points

D

and

E

are taken on sides

AB

and

AC

respectively. (i) State the Basic Proportionality Theorem and its converse. (ii) If

AD=4\text{ cm}

DB=6\text{ cm}

AE=5\text{ cm}

and

EC=7.5\text{ cm}

, examine whether

DE

can be parallel to

BC

. Give full justification. (iii) Suppose a student measures

AE

5.1\text{ cm}

by mistake while all other measurements remain the same as in part (ii). Show clearly whether the conclusion about

DE\parallel BC

still holds. Identify the exact ratio that fails, if any.