**CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.4 Question 5**

**5.** D, E and F are respectively the mid-points of sides AB, BC and CA of . Find the ratio of the areas of and .

**Solution:**

**Given**: D, E and F are mid-points of sides AB, BC and AC of .

**{Given}**

Therefore, by Converse of Basic Proportionality theorem, DF || BC. **(1)**

**{Given}**

Therefore, by Converse of Basic Proportionality theorem, EF || AB. **(2)**

From **(1)** and **(2)**, we can say that **DFEB** is a parallelogram.

** {A quadrilateral is a parallelogram if both the pairs of opposite sides are parallel}**

Similarly, we can prove that **DECF **is a parallelogram.

In and

{**DECF is a parallelogram}**

**{DFEB is a parallelogram}**

Therefore, by **AA similarity criterion**, ~

**{The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides}**

**{FE = BD because DBEF is a parallelogram}**