Question

Prove that the ratio of area of two similar triangle is equal to the rtio of the square of there coeresponding side

Answer 1

answer of this is here

Answer 2

heya friends ✅==♥


Here is ur answer ....
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Given -∆ABC~∆DEF.

To proove ar(∆ABC)/ar(∆DEF)=AB^2/DE^2=WC^2/EF^2

construction--Draw AL perpendicular BC and DM perpendicular EF.

proofe-- ---Since ∆ABC~∆DEF,.....if follow that they are equiangular and their sides are proportional .

•°•<A=<D, <B=<E, <C=<F And..AB/DE=BC/EF=AC/ DF.............1)

now ,(ar∆ABC)=(1/2*BC*AL)

and ar(∆DEF)=(1/2*EF*DM)

•°•ar(∆ABC)/ar(∆arDEF)=1/2*BC*AL/1/2*EF*DM

=BC/EF×AL/DM................2)

Also...

AL/DM=BC/EF.............3)

[•°• in similar triangle,the ratio of the corresponding side is the same as the ratio of corresponding altitutes】

=>using 3) in 2) we get....

ar(∆ABC)/ar(∆DEF)=AB^2/DE^2

ar(∆ABC)/ar(∆DEF)=AC^2/DF^2

hence ,

ar(∆ABC)/ar(∆DEF)=AB^2/DE^2=AC^2/DF^2=BC^2/EF^2...