D and E are points on sides AB and AC respectively of ∆ ABC such that ar (DBC) = ar (EBC). Prove that DE || BC.

Solution:

If two triangles are on a common base and have equal areas, then they will lie between the same parallel lines.

Let's draw the given triangle ABC.

Given that ar (DBC) = ar (EBC)

Since ΔEBC and ΔDBC are lying on a common base BC and they also have equal areas, therefore, ΔEBC and ΔDBC will lie between the same parallel lines.

Hence, DE || BC proved.

☛ Check: Class 9 Maths NCERT Solutions Chapter 9

Video Solution:

D and E are points on sides AB and AC respectively of ∆ ABC such that ar (DBC) = ar (EBC). Prove that DE || BC.

Maths NCERT Solutions Class 9 Chapter 9 Exercise 9.3 Question 7:

Summary:

If D and E are points on sides AB and AC respectively of such that ar (DBC) = ar (EBC), then DE||BC.

☛ Related Questions:

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