Question

and the perimeter of
one
gle
of Two sides
trian
respectively three times to
corresponding
sponding sides and the perimeter
of
the other side triangle. Are the two
triangle
Similar? Why?
the​

Answer 1

Yes

Let the first ▲ be ▲ABC & the second ▲DEF

Let the first ▲ be ▲ABC & the second ▲DEFlet ABC's sides be a,b,c and DEF's 3a,3b,f

Let the first ▲ be ▲ABC & the second ▲DEFlet ABC's sides be a,b,c and DEF's 3a,3b,fSince 3(a+b+c)=3a+3b+f

Let the first ▲ be ▲ABC & the second ▲DEFlet ABC's sides be a,b,c and DEF's 3a,3b,fSince 3(a+b+c)=3a+3b+f=>3a+3b+3c=3a+3b+f

Let the first ▲ be ▲ABC & the second ▲DEFlet ABC's sides be a,b,c and DEF's 3a,3b,fSince 3(a+b+c)=3a+3b+f=>3a+3b+3c=3a+3b+f=>3c=f

Let the first ▲ be ▲ABC & the second ▲DEFlet ABC's sides be a,b,c and DEF's 3a,3b,fSince 3(a+b+c)=3a+3b+f=>3a+3b+3c=3a+3b+f=>3c=f=> the corresponding sides increase by a factor of 3 in ▲DEF from ▲ABC

Let the first ▲ be ▲ABC & the second ▲DEFlet ABC's sides be a,b,c and DEF's 3a,3b,fSince 3(a+b+c)=3a+3b+f=>3a+3b+3c=3a+3b+f=>3c=f=> the corresponding sides increase by a factor of 3 in ▲DEF from ▲ABC=> ▲DEF ||| ▲ABC (SSS)