By Team Aakash Byju's | 20th January 2023
The better idea to understand what are we asked to prove is that, writing a pictorial representation like the one shown below:
So, from the images, we can write that Given: ΔABC∼ΔDEF, AM and DN are the medians of triangles ABC and DEF respectively.
area(ΔABC)
Prove :
area(ΔDEF)
=
AM
DN
2
2
Since, it is given that ΔABC∼ΔDEF, the corresponding sides are in proportion.
AB
DE
BC
EF
CA
FD
=
=
1
2
BC
=
BM
&
1
2
EF
=
EN
AM bisects BC & DN bisects EF
AB
DE
=
1
2
BC
1
2
EF
=
BM
EN
=>
(Continues)
. .
.
(
)
(Continued)
( ΔABC ∼ ΔDEF)
AB
DE
=
1
2
BC
1
2
EF
=
BM
EN
=>
. .
.
&
m∠B = m∠E
Therefore, ΔABM ∼ ΔDEN
Similarly,
AB
DE
=
AM
DN
Since, ΔABC∼ΔDEF, the ratio of their area will be equal to the square of corresponding sides.
Area of ABC
=
AB
DE
2
2
Area of DEF
Since
=
AB
DE
AM
DN
Area of ABC
=
AM
DN
2
2
Area of DEF
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