Mathematics

Problem

12. Show that the relation

R

defined in the set

A

of all triangles as

R=\left\{\left(T_{1}, T_{2}\right): T_{1}\right.

is similar to

\left.\mathrm{T}_{2}\right\}

, is equivalence relation. Consider three right angle triangles

\mathrm{T}_{1}

with sides

3,4,5, \mathrm{~T}_{2}

with sides

5,12,13

and

\mathrm{T}_{3}

with sides

6,8,10

. Which triangles among

T_{1}, T_{2}

and

T_{3}

are related?