# Ex.9.3 Q7 Areas of Parallelograms and Triangles Solution - NCERT Maths Class 9

## Question

\(D\) and \(E\) are points on sides \(AB\) and \(AC\) respectively of \(\Delta ABC\) such that \(\text{ar }(DBC) = \text{ar }(EBC)\). Prove that \(DE\; \| \;BC\).

Video Solution

Areas Of Parallelograms And Triangles

Ex 9.3 | Question 7

## Text Solution

**What is known?**

\(D\) and \(E\) are points on sides \(AB\) and \(AC\) respectively of such that \(ar (DBC) = ar (EBC).\)

**What is unknown?**

How we can prove that \(DE || BC.\)

**Reasoning:**

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

**Steps:**

Since \(\Delta EBC\) and \(\Delta DBC\) are lying on a common base \(BC\) and also have equal areas, \(\Delta EBC\) and \(\Delta DBC\) will lie between the same parallel lines.

\[\therefore DE\;\| \;BC\]

Video Solution

Areas Of Parallelograms And Triangles

Ex 9.3 | Question 7