In Fig. 6.17, (i)

(i) Let us take EC = x cm

Given: DE || BC

Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.

Now, using basic proportionality theorem, we get:

=

x =

x = 2 cm

Hence, EC = 2 cm

(ii) Let us take AD = x cm

Given: DE || BC

Basic Proportionality Theorem: If a line is parallel to a side of a triangle which intersects the other sides into two distinct points, then the line divides those sides in proportion.

Now, using basic proportionality theorem, we get

x =

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