CBSE NCERT Solutions Chapter 6 Triangles Exercise 6.4 Question 6
6. Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Solution:
Given:
~
. AP is the median to side BC of
and DQ is the median to side EF of
.
{Corresponding sides of similar triangles are proportional}
(1)
{P is the mid-point of BC and Q is the mid-point of EF}
To Prove:
Proof:
{The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides}
(2)
In
and
from (1)
And,
{Corresponding angles of similar triangles are equal}
Therefore, by SAS similarity criterion,
~
Therefore,
(3)
Putting (3) in (2), we get
Hence Proved
jeeva says
very simple
Harish says
bhai accha hai explntion it gud
Yukta mooolchandani says
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Jashan says
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