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}
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