Ex 6.4, 6 Exercise 6.4 Chapter 6 Class 10 CBSE NCERT Maths
Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding medians.
Given: Let ABC ~ PQR
Here AD is median
Hence BD = CD = 1/2 BC
Similarly, PS is median
Hence QS = RS = 1/2 QR
To prove: ( )/( )=( / )^2
Proof:
Given ABC ~ PQR
=
Also,
/ = /
/ =2 /2
/ = /
In &
=
/ = /
~
Hence / = /
Now, since ABC PQR
We know that if two triangles are similar,
the ratio of their area is always equal to
the square of the ratio of their corresponding side
( )/( ) = ( / )^2
( )/( ) = ( / )^2
Hence proved

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.